EBook Problems Prob Rules

EBook Problems Set - Rules for Computing Probabilities

Problem 1

A professor who teaches 500 students in an introductory psychology course reports that 250 of the students have taken at least one introductory statistics course, and the other 250 have not taken any statistics courses. 200 of the students were freshmen, and the other 300 students were not freshmen. Exactly 50 of the students were freshmen who had taken at least one introductory statistics course. If you select one of these psychology students at random, what is the probability that the student is not a freshman and has never taken a statistics course?

• Choose one answer.

(a) 30%

(b) 40%

(c) 50%

(d) 60%

(e) 20%

Answer

 (a)

Problem 2

A box contains 30 pens, where 5 are red, 14 are black, and 11 are blue. If you pick three pens from the box at random without replacement, what is the probability that these three pens will all be black?

• Choose one answer.

(a) 14/30 + 14/30 + 14/30

(b) 14/30 + 13/29 + 12/28

(c) 14/30 x 13/29 x 12/28

(d) 1 - (14/30 x 13/29 x 12/28)

Answer

 (b)

Problem 3

When three fair dice are simultaneously thrown, which of these three results is least likely to be obtained?

• Choose one answer.

(a) All three results are equally unlikely.

(b) Two fives and a 3 in any order.

(c) A 5, a 3 and a 6 in any order.

(d) Three 5's.

Answer

 (a)

Problem 4

Records show that in an introductory chemistry course in a college, 20% of the students get an A, 30% get a B, 40% get a C, and 10% get a D. If you pick three students at random, what is the probability that all three will get an A?

• Choose one answer.

(a) 0.8*0.8*0.8

(b) 0.2*0.2*0.2

(c) 200*0.2*0.2*0.2

(d) 0.2*3

Answer

 (b)

Problem 5

A newly born child is equally likely to be a boy or a girl. What is the probability that in a family of three children there are less than 3 boys?

• Choose one answer.

(a) 0.125

(b) 0.75

(c) 0.875

(d) 0.5

Answer

 (c)

Problem 6

A professor who teaches 300 students in an introductory psychology course reports that 135 of the students have taken exactly one introductory statistics course, 60 have taken two or more introductory statistics courses, and the other 105 have not taken any statistics courses. If you select one of these psychology students at random, what is the probability that the student has taken at least one statistics class?

• Choose one answer.

(a) 0.20

(b) 0.45

(c) 0.65

(d) 0.35

Answer

 (c)

Problem 7

Two fair coins are flipped. The probability that both are heads is:

• Choose one answer.

(a) About 33%

(b) Exactly 25%

(c) Exactly 12.5%

(d) Exactly 50%

(e) Exactly 75%

Answer

 (b)

Problem 8

Two fair coins are flipped. The probability that the second coin is a head, given that the first was a head, is:

• Choose one answer.

(a) Exactly 50%

(b) Exactly 25%

(c) Exactly 75%

(d) Exactly 12.5%

(e) About 33%

Answer

 (a)

Problem 9

In a carnival game, a person can win a prize by guessing which one of 5 identical boxes contains the prize. After each guess, if the prize has been won, a new prize is randomly placed in one of the 5 boxes. If a person makes 4 guesses, what is the probability that the person wins a prize exactly twice?

• Choose one answer.

(a) (0.2)^2/(0.8)^2

(b) 2(0.2)^2*(0.8)^2

(c) 6(0.2)^2*(0.8)^2

(d) (0.2)^2*(0.8)^2

(e) 2!/5!

Answer

 (c)

Problem 10

Suppose that you read that 88% of all college students have working cell phones. If you take a random sample of 20 college students, what are the chances that at least 18 of the 20 will have working cell phones?

• Choose one answer.

(a) 0.88*20

(b) 20!/(18!*2!) (0.88)^18 (0.12)^2

(c) 190*(0.88)^18 (0.12)^2 + 20*(0.88)^19(0.12) + (0.88)^20

(d) 1 - 190*(0.88)^18 (0.12)^2 + 20*(0.88)^19(0.12) + (0.88)^20

(e) None of these values

Answer

 (c)

Problem 11

Express Checkout Researchers report that a quarter of the customers who shop for groceries between 5 P.M. and 7 P.M. use express checkout for 10 items or less. Consider 5 randomly selected customers, and let x represent those who use express checkout. Determine the probability that exactly 2 of the 5 customers use express checkout?

• Choose one answer.

(a) (0.25)^2

(b) 10*(0.25)^2*(0.75)^3

(c) 10*(0.25)^2(0.75)^3 + 5*(0.25)^3(0.75)^2 + 5*(0.25)^4(0.75) + (0.25)^5

(d) Cannot be determined without the data.

Answer

 (b)

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