Bluebook SAT Test Probability and Conditional Probability 15

Question 1

A survey of 500 adults found that 200 exercise daily and 300 do not. Of those who exercise daily, 160 have no chronic illness; of those who do not, 150 have no chronic illness. What is the probability a randomly selected adult exercises daily, given they have no chronic illness?

Accepted Answer

16/31

Answer

No chronic illness = 160 + 150 = 310; P(exercise | no illness) = 160/310 = 16/31.

Question 2

Two fair dice are rolled. What is the probability the product of the two numbers is 12?

Accepted Answer

1/9

Answer

Pairs whose product is 12: (2,6),(3,4),(4,3),(6,2) — 4 outcomes out of 36; P = 4/36 = 1/9.

Question 3

The two-way table shows 450 passengers by travel class and on-time status.

On Time   Delayed
First Class       90       60
Economy          180      120

Are travel class and on-time status independent? Use the data to check.

Accepted Answer

Yes, because P(First Class) × P(On Time) = P(First Class and On Time)

Answer

P(on time | First) = 90/150 = 0.6; P(on time | Economy) = 180/300 = 0.6 — equal, so the events are independent.

Question 4

A bag holds tiles labeled A, B, C, D, and E. Two tiles are drawn without replacement. What is the probability of drawing A first and B second?

Accepted Answer

1/20

Answer

P = (1/5)(1/4) = 1/20.

Question 5

Events F and G are independent with P(F) = 0.4 and P(F or G) = 0.7. What is P(G)?

Accepted Answer

0.50

Answer

P(F or G) = P(F) + P(G) − P(F)P(G) → 0.7 = 0.4 + P(G) − 0.4P(G) → 0.3 = 0.6P(G) → P(G) = 0.5.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Probability and Conditional Probability 15