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Probability Homework Section P4
1. A two-person committee is chosen at random from a group of four men and three women. Find the probability that the committee contains at least one man.
2. Three dice are tossed. Find the probability of a) a sum of 4; or b) a sum greater than 4 (may use complement)
3. A bag contains 6 red balls, 7 white balls, and 10 blue balls. A ball is chosen at random from the bag.
Find the probability of choosing a ball that is not red.
4. One card is selected from a standard deck of 52 playing cards. What is the probability that the card is either a heart or a face card?
5. A jar contains seven white, six blue and ten red marbles. If one marble is drawn at random from the jar, find the probability that a) the marble is white or blue; b) the marble is white or red; c) the marble is blue or red.
6. A person removes two aces and a king from a deck of 52 playing cards and draws, without
replacement, two more cards from the deck. In this game, order will matter because the person looks at each card as it is drawn. Drawing an ace of diamonds and then an ace of hearts is a different result than drawing an ace of hearts and then an ace of diamonds.
Find the probability that the person will draw two aces or two kings or an ace and a king.
7. A coin and a die are tossed. Find the probability of getting a tail on the coin or a 3 on the die.
8. A survey claims that 70% of the households in a certain town have a color TV, 20 % have a microwave oven, and 2% have both a color TV and a microwave oven. Find the probability that a randomly selected household has either a color TV or a microwave oven.
9. The following table shows the probability that a customer at a department store will make a purchase in the indicated price range.
Cost Probability
Below $5 .25
$5 - $19.99 .37
$20 - $39.99 .11
$40 - $69.99 .09
$70 - $99.99 .07
$100 - $149.99 .08
$150 or more .03
Find the probability that a customer makes a purchase that is a) less than $20 b) more than $99.99
c) $40 or more d) less than $100
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10. The law firm of Able, Barron, Chalmers, Dowd, Erickson, and Franks has two senior partners: Able and Barron. Two of the attorneys are to be selected to attend a conference. Assuming all are equally likely to be selected find each probability.
a) Chalmers is selected b) Able and Dowd are selected c) At least one senior partner is selected
11. A survey of 282,549 freshmen from the class of 2006 at 437 baccalaureate colleges and universities gave the following information:
# of Colleges Applied to
1 2 or 3 4-6 7 or more
Percent(as decimal) .20 .29 .37 .14
Source: Higher Education Research Institute, UCLA, 2002
Find the probability of each event:
a) The student applied to fewer than 4 colleges.
b) The student applies to at least 2 colleges.
c) The student applied to more than 3 colleges.
d) The student applied to no colleges.
12. Forty-three percent of the world’s population have type O blood, 85% of the world’s population are Rh-positive, and 37% have type O blood and are Rh-positive. What is the probability that any
individual will have type O blood or be Rh-positive?
13. According to the National Safety council, in 1994 there were 38,166 firearm deaths in the United States. Of these, 32,694 were males, 10.954 were between the ages of 15 and 24, and 9809 were males between the ages of 15 and 24.
a) What is the probability that a random person killed by firearms in 1994 was male or between the ages of 15 and 24?
b) What is the probability that a random person killed by firearms in 1994 was neither male nor between the ages of 15 and 24?
14. Suppose 37% of those polled approve of the Republican candidate for president, 42% approve of the Democratic candidate for president, and 7% approve of both candidates. What is the probability that a randomly selected person approves of neither candidate?
15.According to the American Medical Association, in 1996 there were 737,764 physicians in the US.
157,387 were female, 133,005 were under the age of 35, and 47,348 of those under 35 were female.
What is the probability that a randomly chosen physician in 1996 was female or under the age of 35?
16. Suppose that at a college, 53% of the students earn a degree at the end of four years, and 25% of the
students earn a degree at the end of 5 years. What is the probability of earning a degree at the end of 4
or 5 years?
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17. Suppose 18% of the students at a college have an academic scholarship that pays partial tuition, 43% of the students at the college have some need-based financial aid, and 52% of the students have need-based financial aid or an academic scholarship. What is the probability that a randomly selected student has both need-based financial aid and an academic scholarship?
18. Based on research conducted after the 1989 Loma Prieta earthquake, US Geological Survey (USGS) results indicate that there is a 62% probability of at least one quake of magnitude 6.7 or greater striking the San Francisco Bay region before 2032.
a) If there is a 29% probability of two or more earthquakes of magnitude 6.7 or greater in that area before 2032, what is the probability of having exactly one earthquake of magnitude 6.7 or above in that area before 2032?
b) What is the probability of no earthquake of 6.7 or above in the area before 2032?
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Answers
1. (E’ would be a committee with no men) P(E’) = . So P(E) =1- =
7 62. a)
2163
; b) (use complement, E’ = sum less than or equal to 4) P(E) =
54 533. E = not red; E’= red; P(E’) = . P(E) = 1- P(E’) = 1- .
4. The “or “ means we want the union, so P(heart or face) = P(heart) + P(face) – P(heart and face) = .
5. (Note that these are mutually exclusive, so there is no overlap)
23 )16 23 )17 23,
)13 b c a
6. (These are mutually exclusive) P(2 Aces) = = P(2 Kings) = P(Ace and king) = , So P(2 Aces or 2 kings or an ace and a king) = .
7. Note that the results are ordered pairs with a die result and a coin toss result in each order pair, such as (t,1) (t,2) etc. P(tail) + P(3) – P (t ∩ 3) =
2 1
+
6 1
-
12 1
=
12 7
8. P(TV U Microware) = P (TV) + P(Micro) – P(TV ∩Micro) = 0.7 + 0.2 – 0.02 = 0.88 9. a) 0.62 b) 0.11 c) 0.27 d) 0.89
10. a) Put Chalmers on and then choose one more n(E) = 1∙ C(5,1) = 5; n(S) = C(6,2) = 15; P(E) = 1/3 b) If you put both on you are done (there is only one way to do this) n(E) = 1; n(S) = 15; P(E) = 1/15 c) Either one partner or both are on. One senior partner: choose one of 2: C(2,1) and then choose second person C(4,1); so P(one senior partner) = . Put both on: P(both) = ; So P(at least one S.P) = .
11. a) 0.49 b) 0.8 c) 0.51 d) 0
12. P(type O or Rh positive) = P(type O) + P(Rh positive) – P( O & Rh positive) = 0.43 + 0.85 – 0.37 = 0.91.
13. a) P(Male) + P( 15-24) – P(Male and 15-24) = ≈ 0.887.
b) use complement: P(neither) = 0.113
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