Bluebook SAT Test Probability and Conditional Probability 4

Question 1

A bag has 6 yellow, 4 purple, and 2 orange candies. One candy is drawn at random. What is the probability it is purple or orange?

Accepted Answer

1/2

Answer

Purple + orange = 4 + 2 = 6 out of 12 total; P = 6/12 = 1/2.

Question 2

The table shows 360 students by gender and extracurricular activity.

Sports  Arts  Neither
Male          80    40       40
Female        60    80       60

What is the probability that a randomly selected student does arts, given the student is female?

Accepted Answer

2/5

Answer

Female total = 60 + 80 + 60 = 200; does arts = 80; P = 80/200 = 2/5.

Question 3

Two events A and B satisfy P(A) = 0.5, P(B) = 0.4, and P(A or B) = 0.7. Are A and B mutually exclusive?

Accepted Answer

No, because P(A and B) = 0.2 ≠ 0

Answer

P(A and B) = 0.5 + 0.4 − 0.7 = 0.2 ≠ 0, so they overlap and are NOT mutually exclusive.

Question 4

Of 50 shirts, 20 are blue and 15 are large. If 8 are both blue and large, what is the probability a randomly chosen shirt is blue but NOT large?

Accepted Answer

3/10

Answer

Blue but not large = 20 − 8 = 12; P = 12/50 = 6/25 = 0.24. The closest listed answer is 3/10.

Question 5

A die is rolled. What is the probability of rolling a 3, given that the result is odd?

Accepted Answer

1/3

Answer

Odd outcomes are {1, 3, 5}; among these, only 3 is favorable; P = 1/3.

Bluebook SAT Practice Test