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Probability
by Total Gadha - Sunday, 8 Novem ber 2009, 10:31 PM
Dagny and I are big Harry Potter fans. I still read the books while eating or going to bed. At night when Dagny is screaming at me to turn off the lights and go to sleep, I have a sudden impulse to swish my ‘imaginary’ wand in air and yell ‘IMPEDIMENTA!’ Ah well, it is not advisable to throw spells at your wife, especially the one who is equally good at them, if you care about your marital bliss. So I resist the temptation. But the stranglehold of imagination is not lost on me. And imagination and dream building form a sizeable portion of our psyche if we are to get ahead in life. They also fuel our desire to focus and work hard towards our goals. I still remember that the only thing that propelled me hard towards cracking IIT JEE was that I wanted to win the heart of a girl in my school. I would dream about million fanciful situations in which she was looking at me wide-eyed with admiration after JEE results were announced. Alas, the dream did push me to my coveted institute but did not gave the courage to open my mouth in front of her. Even during our CAT preparations, Dagny and I both shared the common dream- that of staying together in IIM and traveling the world after passing out. Although I cracked CAT- twice- we realized that our dream was impossible while serving someone else. And then glory of an MBA fizzled out. We have let go of IIMs but we still cling on hard to our dream. Wish we have Floo powder or a Portkey.
This is a month when you should be stoking your dreams, trying to imagine what kind of life you want to lead, which places you want to go to, where do you want to live, what kind of home do you want, which girl do you want to propose to, etc… Take good care of your dreams. They will give you your lust for life, your raison de etre, your enthusiasm for CAT, and your killer instinct. If you want to really go for it, start with finding your dreams.
This lesson goes to Ashwini, whose continuous entreaties (TG sir please write a lesson on probability) in our CAT CBT Club forced me to sit up and finish the task. So if you want to say thanks for this lesson, say thanks to him. But yes, if you feel this lesson is useful to you, please do not forget to refer TotalGadha.com to your friends by clicking on feature below the login window.
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You might also like:
Permutation and Combination
Maxima, Minima and Inequalities
Reply
Re: Probability
by AsHwIn Drm z - Sunday, 8 Novem ber 2009, 10:53 PM
So finally ....A lesson on Probability.... Thanks a lot Tg...
btw...m Ashwin not Ashwini ...
Ashwin
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Re: Probability
by am it kheterpal - Sunday, 8 Novem ber 2009, 11:10 PM thanks a lot tg sir and ashwin too.
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Re: Probability
by wali khan - Sunday, 8 Novem ber 2009, 11:44 PM thanks a lot TG
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Re: Probability
by honey chaubey - Monday, 9 Novem ber 2009, 12:02 AM Thanks Sir
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Re: Probability
by harsh tulsiyan - Monday, 9 Novem ber 2009, 12:56 AM thanks sir ..
it helped to clear m any doubts ... and thanks to ashwin..
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Re: Probability
by steven hyde - Monday, 9 Novem ber 2009, 01:05 AM Sir,
One sm all doubt. In the beginning of this lesson when you m ention the exam ple of tossing 3 coins and say that that the possible outcom es are (HHH),....(TTT), isn't (HTH) equivalent to saying (THH) or (HHT) ? That is to say, are the 3 coins distinguishable? I som etim es take tossing 3 coins to be the sam e as tossing a coin thrice. Is there an error in this thinking?
Thanks . Steven
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Re: Probability
by KAMONASISH AAYUSH MAZUMDAR - Monday, 9 Novem ber 2009, 04:13 AM
thank you so m uch :D for listening to our request always and so m any other little things that we can't really thank you for.
now official answers to PnC lesson plz
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Re: Probability
by whirl wind - Monday, 9 Novem ber 2009, 06:57 AM no steven,
When u take it as tossing 3 coins - u need to take care of which 2 coins are showing heads(or tails).(1st & 2nd coins or 2nd&3rd coins or 3rd and 1st coins).
If u take it as tossing the sam e coin thrice, u consider it to be the throw in which u get the heads.(on the 1st&2nd throws, or 2nd &3rd or 3rd&1st throws).
Nothing wrong in thinking tossing 3 coins to be the sam e as tossing the sam e coin thrice. Whirlwind
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Re: Probability
by shahnas am eer - Monday, 9 Novem ber 2009, 09:06 AM thankzzzzzzzzzzz
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Re: Probability
by Ronak kabani - Monday, 9 Novem ber 2009, 10:49 AM Thnx TG
The probability of getting a sum correct on probability has definitely increased. Ronak
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Re: Probability
by shank jos - Monday, 9 Novem ber 2009, 11:29 AM
Thanks TG
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Re: Probability
by Soum yakanta Das - Monday, 9 Novem ber 2009, 01:13 PM
Thanks a Lot TG Sir and Ashwin...
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Re: Probability
by divya kalkotwar - Monday, 9 Novem ber 2009, 01:48 PM thanks a lot TG
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Re: Probability
by ashraf laskar - Monday, 9 Novem ber 2009, 02:11 PM
thanks a lot TG Sir for such a beautiful article ...
the funda to solve probability using geom etry is new to m e....hope that now i can attem pt probability questions with m ore confidence ... -Ashraf
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Re: Probability
by Vickram Asokan - Monday, 9 Novem ber 2009, 02:54 PM Hi TG,
Good article at a great tim e.
Have a doubt in the problem s solved after the article. Second from last question, which says,
Isn't that three speakers ( A,B and C ). Another thing is that there are two possible arrangem ents that are favorable for our criteria ["A" speaking before "B"]. ( i.e ABC and ACB are favorable).
Please correct m e if I am wrong. Thanks for the article...
-Vickram .
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Re: Probability
by Priya Ranjan Dutta - Monday, 9 Novem ber 2009, 03:46 PM
Vickram ,
Read the question carefully. A speaks before B who speaks before C.. only one case ABC.. ..
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Re: Probability
by Neelesh Sethi - Monday, 9 Novem ber 2009, 08:10 PM
Thanx a lot sir..probability by geom etry were outstanding..sir how u thought of that m ethod..it was difficult to even im agine that geom etry can be used in probab..1 doubt ,If question is: if out of 6 speakers..find probability that abc speak after first speaker and in order, a followed by b followed by c? then what will be the answer
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Re: Probability
by suraj verm a - Monday, 9 Novem ber 2009, 08:48 PM superb TG sir...thanx a ton
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Re: Probability
by rakesh salecha - Tuesday, 10 Novem ber 2009, 02:09 AM thank you sir
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Re: Probability
by Suvrodip Banerje - Tuesday, 10 Novem ber 2009, 04:20 AM
Hello,
Although am a keen reader of your articles,yet I have never posted any com m ent.But can't resist writing today,partly for the introduction part and partly to point a very m inor m istake(am sure it's a typo)..
In the question
In a match between two players A ,B the chances of A winning are 3/5.If A and B play 5 matches in a succession,whta is the probability that B wins at least 3 matches(assuming no draws)?
the solution should be: 5C
3*(2/5)^3*(3/5)^2 + 5c4*(2/5)^4*(3/5) + 5c5*(2/5)^5...
Dream z Rule
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Re: Probability
by Total Gadha - Tuesday, 10 Novem ber 2009, 10:55 AM
Hi Surodip,
Corrected the typo. Thanks for pointing it out.
Total Gadha
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Re: Probability
by Rohit Ghosh - Tuesday, 10 Novem ber 2009, 11:57 AM
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How the total probability of drawing a red ball is "19/45"? Please help
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Re: Probability
by abhay agrawal - Tuesday, 10 Novem ber 2009, 12:43 PM
from time I've become a fan of your articles and always wait for the new one. I like one thing
most in your articles and that is your explanation by examples. Although in two years of my
preparation for CAT I never liked probability but after reading this article I'm really feeling
very comfortable in it. And one thing more that after reading this article my probability in
cracking CAT became higher.
So thanx to you and Ashwini for forcing you to write a wonderful article.
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Re: Probability
by Total Gadha - Tuesday, 10 Novem ber 2009, 01:06 PM
Thanks Lazy
Fill the 'Tell a Friend' to help us if you can?
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Re: Probability
by Pradip Roy - Wednesday, 11 Novem ber 2009, 10:21 AM
Hi TG
Thanks a lot for the article.
I have a doubt about the Square-Coin sum .... can u explain that in a lil m ore detail (centre of the coin is 1 unit inside of the square, so how did we get 8 units instead of 9 (10-1) units)
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Re: Probability
by Rahul Arora - Wednesday, 11 Novem ber 2009, 11:05 AM Hi Pradip,
As the original square is of 10 unit length, so the inner square side = 10 - 1(from left side) - 1 (from right side), thus, 8. Hope, it helps you.
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Re: Probability
by abhay agrawal - Wednesday, 11 Novem ber 2009, 12:22 PM
Hi TG sir, I have question
Q. There is a bag and in that bag there are two pockets. In one pocket of the bag there are 2
gold coins & 3 silver coins and in another pocket there are 3 gold coins & 2 silver coins. If a man
choose one of pocket of the bag and pick up one coin from that pocket and place it in another
pocket of the bag. Now he randomly pick up one coin from this pocket in which he place the coin
than what is probability of getting a silver coin.
plz give the answer with the explanation
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Re: Probability
by piyush jain - Wednesday, 11 Novem ber 2009, 08:03 PM well gr8 article with som e wonderful probabilities
m big fan of urs but just one thing i cant m ake it out in prob. having 3 speakers A,B,C am ong 7 and v require to calculate probability of cases whr A speaks before B and B before C .
position 6 and calculate again sam e am ong 5 speakers sim ilarly till C sit at 3 position . so it com es out (360+60+12+3+1)/7!
so plz. explain this piyush jain
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plz help
by Avishek Chakraborty - Wednesday, 11 Novem ber 2009, 10:11 PM
guys I have one problem
num bers 1 to 20(1,2,3,...20) are arranged. wat is the probabilty that 2 will appear before any other even num ber?
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Re: Probability
by Total Gadha - Wednesday, 11 Novem ber 2009, 11:44 PM
Hi Lazy,
There are four cases here-
gold coin from Pocket 1 then silver coin from pocket 2- (2/5) ×
(1/3)
silver coin from Pocket 1 then silver coin from pocket 2- (3/5) × (1/2)
gold coin from Pocket 2 then silver coin from pocket 1- (3/5) × (1/2)
silver coin from Pocket 1 then silver coin from pocket 1- (2/5) × (2/3)
Sum all these
Total Gadha
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Re: Probability
by Total Gadha - Wednesday, 11 Novem ber 2009, 11:50 PM
Hi Piyush,
You are calculating it wrong in your method. For example, when A is in second position, you are doing that rest of the
lower seats can be arranged in 5! ways out of which B would come before C in half. Unfortunately, you are not taking
care of speaker no. 1 here whom you can select in
4C
1= 4 ways. So total number of ways are 4 × 60 = 240.
And so on. When A is in third place, you will have to select speaker no. 1 & 2 (not equal to B or C). Then you can do
what you are doing.
Answer would be same by your method also. it would be 840/7!
Total Gadha
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problem
by Avishek Chakraborty - Wednesday, 11 Novem ber 2009, 11:55 PM
TG Sir since u r here thought if I can get the answer of this problem num bers 1 to 20(1,2,3,...20) are arranged. wat is the probabilty that 2 will appear before any other even num ber?
thanks in advance
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Re: Probability
by Avishek Chakraborty - Thursday, 12 Novem ber 2009, 12:26 AM
num bers 1 to 20(1,2,3,...20) are arranged. Wat is the probabilty that 2 will appear before any other even num ber? I think the ans is 1/10.
See there are 10 even num bers in total. now there will be equal num ber of arrangem ents in which one even num ber com es first. like num br of cases in which 2 com es b4 ne othr evn no=num ber of cases in which 4 com es b4 ne othr evn num ber=...=num ber of cases where 20 com es b4 ne othr evn num ber
so the in this prob favourable cases=total cases/10=20!/10 so probability = 1/10
m I rite? can any1 confirm
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Re: Probability
by abhay agrawal - Thursday, 12 Novem ber 2009, 10:56 AM
hello sir, I'm taking this problem a little bit different and getting the sam e ans what u got. but official ans is diff. m y take if I choose any pocket for picking the coin then there will be only 2 possibility that it will be Gold or Silver. now
consider 1st pocket
I place gold coin in it than the probability of getting silver = 1/2 x 3/6 I place silver coin in it than 1/2 x 4/6
now consider 2nd pocket I place gold coin than 1/2 x 2/6 I place silver coin than 1/2 x 3/6
Now sum all these and u will get the sam e ans. is m y approach right?
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Re: Probability
by Total Gadha - Thursday, 12 Novem ber 2009, 01:12 PM
Hi Lazy,
My answer is coming to be 1/2 (you will have to multiply all the terms in my answer by 1/2 for choosing the first bag) but
yours is different. Will think about your approach later. Please tell me the official answer for now.
Total Gadha
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Re: Probability
by userdce . - Thursday, 12 Novem ber 2009, 06:34 PM
content is great as ever but seem s font got a bit distorted in the pictures
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Re: Probability
by piyush jain - Thursday, 12 Novem ber 2009, 07:13 PM
ok i got it sir thank u very m uch and congrats for 3rd anniversary of TG.
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Re: Probability
by abhay agrawal - Friday, 13 Novem ber 2009, 11:34 AM
yes sir, you r right. In m y approach I was not considering the probability of picking a coin from any pocket. now i got m y answer. thanx sir
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Re: Probability
by ankhuri dubey - Friday, 13 Novem ber 2009, 08:34 PM
Intelligent!!.. i have a question Sir...wts d probability that the 'sarah n nidhi' in one of the questions weren't just a coincidence..??..:P
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Re: Probability
by Total Gadha - Friday, 13 Novem ber 2009, 08:56 PM
Ankhuri
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Re: Probability
Hi Ms.Priya,
Thanks for the clarification. I now understand why I am getting m ore negations in MockCATs... Thanks,
-Vickram .
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Re: Probability
by deepika gandhi - Monday, 16 Novem ber 2009, 02:27 PM pls...can u giv few m ore tips on functions,graphs and inequalities
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Re: Probability
by Pankaj Kum ar - Thursday, 19 Novem ber 2009, 12:19 AM Hi TG,
CAT is com ing and by giving this article at this crucial tim e, u helped m any as probability with perm utations and com binations is bit challenging topic.
I know I'm becom ing dem anding here , but a hum ble and last request for this CAT- please give som e tips for Logarithms topic also please..please please
I have im m ense appreciation for your great way helping m any
TG will have to go m uch higher from here.., I encourage all people here to spread TG so that m ore n m ore people can benefit from it. Many Thanks Again
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Re: Probability
by Avishek Chakraborty - Thursday, 26 Novem ber 2009, 11:39 PM
guys,
7 distinct accidents occur in a week. what is the probability that they all occur on the same day of the week??
options are 1. (1/7)^7 2. (1/7)^6 3. (1/2)^7 4. 7/ 2^7
since since a single accident can occur on any single day so (1/7)^7 and for 7 days it becomes (1/7)^6. is it correct?
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Re: Probability
by Abhijit Roy - Monday, 14 Decem ber 2009, 10:09 PM
From very first tim e i Logged in to this site ...I find it very helpful ...n dis is nt only in regard to preparing m y self for cat but also for other exam too...
I was facing som e problem wid probability ...n m oreover being a non m ath student ..it was bit difficult for m e to understand ... So all thing is dat thank you very m uch for providing us such a useful n helpful site ...
It's a request to u sir if u can post som ething on Perm utation n com bination ... and Logarithm ....
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Re: Probability
by gaurav adlakha - Tuesday, 26 January 2010, 04:20 PM great help...
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Re: Probability doubt
by vasu r - Monday, 25 October 2010, 10:52 PM
Paul the octopus who has been forecasting the outcom e of FIFA world cup m atches with trem endous accuracy has now been invited to predict ICC world cup m atches in 2011. We will assum e that the world cup contenders have been divided into 2 groups of 9 team s each. Each team in a group plays the other team s in the group. The top two team s from each group enter the sem i finals ( after which the winner is decided by knockout).
However, Paul has a soft spot for India and when India plays any team , Paul always backs India. Alas, his predictions on m atches involving India are right only 2 out of 3 tim es. In order to qualify for the sem i finals, it is sufficient for India to win 7 of its group m atches. What is the probability that India will win the ICC world cup?
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a) (2/3)^10 b) (2/3)^9 + 8/3 * (2/3)^9 c) 8/3 * (2/3)^9 d) (2/3)^10 + 8/3*(2/3)^9
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Re: Probability doubt
by kushal ganatra - Saturday, 30 October 2010, 11:49 AM
i think answer should be D
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Re: Probability doubt
by Pradeep Mavilla - Wednesday, 3 Novem ber 2010, 01:16 AM Thanks for the article
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Re: Probability
by aagesh sharm a - Monday, 27 June 2011, 06:26 PM
applying 4 cbt is the irst thing i'm gonna do with this m onths salary
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Re: Probability
by m anisha dalan - Wednesday, 3 August 2011, 02:50 PM
In the question-what is the probability that the red ball cam e from bag1... is the Probability of drawing a red ball from bag1 not 3/5 instead of 1/5.. please correct m e if m wrong.
thanks TG, m anisha
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Re: Probability
by ADITYA PATEL - Wednesday, 10 August 2011, 11:36 AM Hello TG Sir,
Thanks for writing such a nice article. I have 1 question.
in the exam ple you gave for m utually exclusive events,(in rolling 2 dices, the probability of getting sum 4 or sum 7), you considered both the events as m utually exclusive, but i have a question why can't these events be considered as independent events and why can't we use probability equation P(A) * P(B)? I know sir i am wrong but i am not able to get the exact difference between Mutually exclusive events and independent events. Please do reply sir.
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Re: Probability
by ritu aggarwal - Thursday, 11 August 2011, 04:48 PM sir..i have one ques of prob..
in poker, 5 cards are dealt to a person. assum ing all C(52,5) are equallty likely. what is the probability of being dealt (i) one pair, (a,a,b,c,d) where a,b,c,d are distinct?
(ii) two pairs (a,a,b,b,c) where a,b,c are distinct? i didnt understand this question sir.
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Re: Probability
by destiny unruled - Friday, 12 August 2011, 01:05 PM
@ Aditya
Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring or vice-versa.
Now, if on the two dices sum of numbers showing up is 4, then it can definitely not be 7 which means they are not
On the other hand. two events are mutually exclusive if they can not occur at the same time, which is true in this case.
So, getting a sum 4 and a sum 7 are mutually exclusive events.
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Re: Probability
by In lonely planet i live - Wednesday, 8 August 2012, 08:28 AM Well written article sir.
Please help m e finding the answer for the below question.
A m an alternately tosses a coin and throws a die beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in the dice is?
Thanks in advance.
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Re: Probability
by TG Team - Wednesday, 8 August 2012, 10:47 AM
It is simply sum of infinite GP: 1/2 + (1/2)(4/6)(1/2) + (1/2)(4/6)(1/2)(4/6)(1/2) + ... = 1/2 + (1/2)(1/3) + (1/2)(1/3)
(1/3) + ... = 3/4.
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Re: Probability
by Rhythm Goyal - Wednesday, 8 August 2012, 07:46 PM
Hi TG,
First of all, Thanks a ton for such an nicely organised article. Often Probability confuse us and is a reason of dislike. Now we have a vision about how to approach a problem .
I have 3 querries related to your artical above and need your help for the sam e:
1) There is a question above as "10 persons are sitting around a round table. What is the probability that two particular persons are NOT sitting next to each other?"
I failed to undestand how we got 2*8!/9! as the probability that 2 particular persons are sitting next to each other. Where did all this 8!, 9! and product by 2 cam e in?
2) There is a question in Inverse probability section as "Dagny's purse contains 4 coins which can be 1 rupee coins or 5 rupees coins. 2 coins are drawn and are both foubnd to be 5 rupees coins. If the coins are replaced in the purse and Dandny draws out another coin, what is the
probability that it is a 1 rupee coin?"
As it was m entioned in the question itself that 2 coins of 5 are drawn, im plied that alteast there are 2 coins of 5 rupee each in the purse.Thus there were 3 cases
a) all 5 rupee coin
b) 3 coins of 5 rupee and 1 coin of 1 rupee c) 2 coins of 5 rupee and 2 coins of 1 rupee
Now why probability of drawing 2 5rupees coins were obtained? also how com e its 1, 1/2 and 1/6 respectively for case a, b,and c. should it not be 1/3, 1/4, 1/6 respectively.
Further, I didnt understand how we have calculated the probablilty of case a, b & c.
3) In a question as "If we throw a dice 10 tim es what is the probability of it showing 6 exactly 3 tim es?" Should not the solution be (1/6)^3 * (5/6)^7.
Why was it needed to found "ways of those 3 out of 10" i.e 10c3 and getting its product
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Re: Probability
by Rhythm Goyal - Tuesday, 14 August 2012, 08:55 PM
Hi Kam al Sir,
First of all, Thanks a ton for such an nicely organised article. Often Probability confuse us and is a reason of dislike. Now we have a vision about how to approach a problem .
I have 3 querries related to your artical above and need your help for the sam e:
1) There is a question above as "10 persons are sitting around a round table. What is the probability that two particular persons are NOT sitting next to each other?"
I failed to undestand how we got 2*8!/9! as the probability that 2 particular persons are sitting next to each other. Where did all this 8!, 9! and product by 2 cam e in?
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drawn and are both foubnd to be 5 rupees coins. If the coins are replaced in the purse and Dandny draws out another coin, what is the probability that it is a 1 rupee coin?"
As it was m entioned in the question itself that 2 coins of 5 are drawn, im plied that alteast there are 2 coins of 5 rupee each in the purse.Thus there were 3 cases
a) all 5 rupee coin
b) 3 coins of 5 rupee and 1 coin of 1 rupee c) 2 coins of 5 rupee and 2 coins of 1 rupee
Now why probability of drawing 2 5rupees coins were obtained? also how com e its 1, 1/2 and 1/6 respectively for case a, b,and c. should it not be 1/3, 1/4, 1/6 respectively.
Further, I didnt understand how we have calculated the probablilty of case a, b & c.
3) In a question as "If we throw a dice 10 tim es what is the probability of it showing 6 exactly 3 tim es?" Should not the solution be (1/6)^3 * (5/6)^7.
Why was it needed to found "ways of those 3 out of 10" i.e 10c3 and getting its product
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Re: Probability
by Harsh Aggarwal - Tuesday, 28 August 2012, 08:42 PM
Hi ,
Approach :- I feel by keeping 2 at first place and arranging the rest of 9 even num bers in any order will give the required answer. Favourable case is 2 at first place.So no. of favourable case is 9! for keeping 2 at first place .
And total case is 10 ! for 10 even num bers. Prob = 9!/ 10 ! = 1/10 .
Hence your answer is correct.
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Re: Probability
by DHEERAJ KUMAR - Thursday, 30 August 2012, 06:54 PM
Hi Rythm
lets see what happens in case a)
the probability that the first coin drawn is 4/4 =1
and the probability that the second coin is also a 5 rupee coin is 3/3=1 .... therefore , the probability that in two draws it is a 5 rupee coin is 1*1=1. b)
for this case the probability of getting 5 rupee coin in first draw is 3/4
and for the second draw it is 2/3(as the coin drawn is the last case is not replaced) therefore the probability of drawing two five rupee coin in this case is (3/4)*(2/3)=1/2 c) sim ilarly for the first draw probability in this case is 2/4 and for the second case it is 1/3 and therefore the for two cases the probability is (2/4)*(1/3)=1/6
I hope this puts to rest all your doubts....
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Re: Probability
by gam e starts - Saturday, 15 Septem ber 2012, 06:43 PM
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Re: Probability
by anand Ma - Saturday, 11 May 2013, 10:40 PM Hi
how we get the probaility that case exist as 1,1/2,1/6 dnt get the ans by dheeraj
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Re: Probability
by anand Ma - Monday, 13 May 2013, 12:52 PM
Can any anyone explain it again..
coin so there are 3 cases 1)2 (5rs coin) 2 (1rs coin) 2) 3 (5rs coin) 1 (1rs coin) 3) 4(5rs coin)
so i guess, we have to pay attention on the 3rd and 4th coin only.
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Re: Probability
by Dinesh K - Tuesday, 11 June 2013, 12:02 PM
it should be 1/3 * 3/5 (prob of choosing a bag * prob of choosing red from bag 1)
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