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Chapter 4&5_Assignment 3

Name________________________________________________________ Show work to receive full credits!!!!!

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability.

1) A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?

A) 7

9 B)

1

3 C) 12 D)

2 3

1)

2) If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade?

A) 25

52 B)

11

26 C)

1

22 D)

9 26

2)

3) A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 7 wood and 14 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.

A) 0.535 B) 0.105 C) 0.57

D) There is insufficient information to answer the question.

3)

4) Of the 64 people who answered "yes" to a question, 6 were male. Of the 70 people that answered "no" to the question, 8 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?

A) 0.582 B) 0.094 C) 0.104 D) 0.537

4)

5) A study of consumer smoking habits includes 198 people in the 18-22 age bracket (40 of whom

smoke), 125 people in the 23-30 age bracket (31 of whom smoke), and 90 people in the 31-40

age bracket (30 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes.

A) 0.472 B) 0.075 C) 0.547 D) 0.248

5)

6) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9).

A) 2

13 B) 7 C)

13

2 D)

7 26

6)

7) A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).

A) 3

10 B)

7

10 C) 7 D)

10 7

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8) The probability that an event will occur is 0.3. What is the probability that the event will not occur?

A) 0 B) 3

7

C) 0.7 D) None of the above is correct.

8)

Is Event B dependent or independent of Event A?

9) A: A green ball is drawn from a box with five balls and placed next to the box. B: A red ball is drawn next and placed next to the green one.

A) Independent B) Dependent

9)

Determine whether the events are disjoint.

10) Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass.

A) Yes B) No

10)

11) Get a full time day job as a teller with a bank. Get a full time day job as a cashier at a store.

A) Yes B) No

11)

Find the indicated complement.

12) The probability that Luis will pass his statistics test is 0.49. Find the probability that he will fail his statistics test.

A) 2.04 B) 0.96 C) 0.25 D) 0.51

12)

13) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

A) 334

365 B)

31

334 C)

31

365 D)

11 12

13)

14) Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.428. Find the probability that in a given year it will not snow on January 1st in that town.

A) 2.336 B) 1.428 C) 0.572 D) 0.748

14)

Find the indicated probability.

15) In one town, 44% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if

necessary.

A) 0.189 B) 0.194 C) 0.880 D) 0.440

15)

16) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.

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17) The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker

Light smoker

Heavy smoker Total

Men 425 38 35 498

Women 381 32 43 456

Total 806 70 78 954

If two different people are randomly selected from the 954 subjects, find the probability that they are both women. Round to four decimal places.

A) 0.2285 B) 0.2282 C) 0.000004809 D) 0.1595

17)

Find the indicated probability. Round to the nearest thousandth.

18) In a batch of 8,000 clock radios 2% are defective. A sample of 11 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected?

A) 0.801 B) 0.0909 C) 0.199 D) 0.0200

18)

19) A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 40 that have no defects. What is the probability that at least one of the calculators is defective?

A) 0.785 B) 0.215 C) 0.774 D) 0.180

19)

20) A study conducted at a certain college shows that 57% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 9 randomly selected graduates, at least one finds a job in his or her chosen field within a year of

graduating.

A) 0.994 B) 0.111 C) 0.570 D) 0.999

20)

Find the indicated probability.

21) A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 29 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four decimal places.

A) 7.5098 B) 0.1449 C) 0.1390 D) 0.1463

21)

22) Among the contestants in a competition are 46 women and 23 men. If 5 winners are randomly selected, what is the probability that they are all men? Round to five decimal places.

A) 0.13169 B) 0.03125 C) 0.02455 D) 0.00299

22)

23) What is the probability that 4 randomly selected people all have different birthdays? Round to four decimal places.

A) 0.9729 B) 0.9836 C) 0.9891 D) 0.9918

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Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.

24) The table below shows the soft drinks preferences of people in three age groups. cola root beer lemon-lime

under 21 years of age 40 25 20

between 21 and 40 35 20 30

over 40 years of age 20 30 35

If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and drinks cola.

A) 4

17 B)

4 19

C) 4

51 D) None of the above is correct.

24)

25) The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker

Light smoker

Heavy smoker Total

Men 391 61 65 517

Women 312 72 80 464

Total 703 133 145 981

If one of the 981 subjects is randomly selected, find the probability that the person chosen is a nonsmoker given that it is a woman. Round to the nearest thousandth.

A) 0.318 B) 0.444 C) 0.672 D) 0.373

25)

26) The following table contains data from a study of two airlines which fly to Small Town, USA. Number of flights

which were on time

Number of flights which were late

Podunk Airlines 33 6

Upstate Airlines 43 5

If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight given that it was late.

A) 5

87 B)

5 11

C) 5

48 D) None of the above is correct.

26)

Find the indicated probability.

27) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express your answer as a simplified fraction.

A) 25

51 B)

13

51 C)

25

102 D)

1 2,652

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28) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express your answer as a simplified fraction.

A) 13

102 B)

2

13 C)

4

663 D)

1 663

28)

29) In a homicide case 4 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 4 witnesses would pick the same person.

A) 0.0016 B) 0.008 C) 0.0009766 D) 0.8

29)

30) Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.

A) 0.0082 B) 0.00000002 C) 0.3333 D) 0.00000751

30)

31) In one town, 66% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if

necessary.

A) 0.19 B) 0.66 C) 0.061 D) 2.64

31)

32) When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a

pair of dice are rolled 3 times, what is the probability of getting a sum of 7 every time? Round to eight decimal places.

A) 0.00735168 B) 0.00462963 C) 0.0476 D) 0.00291545

32)

33) A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary.

A) 0.844 B) 0.484 C) 0.428 D) 0

33)

34) A multiple choice test has 12 questions each of which has 5 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?

A) 0.00800 B) 0.764 C) 0.283 D) 0.236

34)

Solve the problem.

35) On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

A) 12.8 B) 4.3 C) 8.5 D) 5.7

35)

36) On a multiple choice test with 29 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

A) 2.3 B) 29.6 C) 54.4 D) 5.4

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37) A company manufactures batteries in batches of 15 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch.

A) 0.4 B) 43.7 C) 0.7 D) 0.2

37)

38) The probability of winning a certain lottery is 1

70,422. For people who play 545 times, find the mean number of wins.

A) 129.2 B) 0.0018 C) 0.000014 D) 0.0077

38)

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than μ - 2σ or greater than μ + 2σ.

39) A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 494 consumers who recognize the Dull Computer Company name?

A) Yes B) No

39)

Find the indicated probability. Round to three decimal places.

40) A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 14 drivers living on one particular street, 3 were involved in a car

accident last year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?

A) 0.094 B) 0.126 C) 0.906 D) 0.393

40)

41) In a study, 44% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 14 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 14 adults are randomly selected, 3 or fewer are in excellent health.

A) 0.053 B) 0.073 C) 0.020 D) 0.046

41)

42) A machine has 11 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working.

A) 0.162 B) 0.839 C) 0.111 D) 0.949

42)

Use the normal distribution to approximate the desired probability.

43) Find the probability that in 200 tosses of a fair die, we will obtain at least 30 fives.

A) 0.7673 B) 0.8871 C) 0.6229 D) 0.5871

43)

44) Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives.

A) 0.4936 B) 0.1871 C) 0.3229 D) 0.2946

44)

Determine whether the events are disjoint.

45) Get stung by a bee. Get stung by a wasp.

A) Yes B) No

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Answer Key

Testname: EXTRA PROBABILITY PROBLEMS

1) D 2) B 3) C 4) D 5) A 6) A 7) B 8) C 9) B 10) B 11) A 12) D 13) A 14) C 15) B 16) B 17) B 18) C 19) A 20) D 21) C 22) D 23) B 24) C 25) C 26) B 27) C 28) C 29) B 30) D 31) A 32) B 33) C 34) D 35) B 36) A 37) C 38) D 39) A 40) B 41) B 42) B 43) A 44) D 45) B

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3/12/2016

If two dice are rolled one time, find the probability of getting these results.

a. A sum of 6 Ans: 5/36

b. Doubles Ans: 1/6 c. A sum of 7or 11 Ans: 2/9

d. A sum greater than 9 Ans: 1/6

e. A sum less than or equal to 4 Ans: 1/6

Section 4-2

a. A kingor a queenor a jack. Ans: 3/13

b. A clubor a heartor a spade. Ans: 3/4

c. A kingor a queenor a diamond. Ans: 19/52

d. An aceor a diamondor a heart. Ans: 7/13

e. A 9or a 10or a spadeor a club. Ans: 15/26

Section 4.3

If one card is drawn from an ordinary deck of cards, find the probability of getting the following:

Sections 4.4 & 4.5

At a local university 54.3%of incoming first-year students have computers. If three students are selected at random, find the following probabilities. a. None have computers

b. At least one has a computer c. All have computers

= 0.0954 = 0.9046

= 0.1601

Consider this table concerning utility patents granted for a specific year. Select one patent at random. a. What is the probability that it is a

foreign patent, given that it was issued to a corporation? b. What is the probability that it

was issued to an individual, given that it was a U.S. patent?

Corporation Government Individual U.S. 70,894 921 6129 Foreign 63,182 104 6267

= 0.4712

References

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