Bluebook SAT Test Probability and Conditional Probability 9

Question 1

A box holds 9 cards numbered 1–9. A card is drawn at random. What is the probability the number is a perfect square?

Accepted Answer

1/3

Answer

Perfect squares in 1–9 are 1, 4, 9 — that's 3 out of 9, which equals 1/3.

Question 2

The two-way table below shows 200 employees categorized by department and remote-work status.

Remote   In-Office
Engineering   40       60
Marketing     30       70

If one employee is chosen at random, what is the probability they are in Engineering and work remotely?

Accepted Answer

1/5

Answer

40 out of 200 employees are Engineering and Remote: 40/200 = 1/5.

Question 3

A bag contains 3 white balls and 7 black balls. Two balls are drawn without replacement. What is the probability both are black?

Accepted Answer

7/15

Answer

P = (7/10)(6/9) = 42/90 = 7/15.

Question 4

In a survey of 400 people, 160 prefer tea, 200 prefer coffee, and 40 prefer neither. What is the probability that a randomly selected person prefers tea, given they have a preference (i.e., they don't prefer neither)?

Accepted Answer

2/5

Answer

Those with a preference: 400 − 40 = 360; P(tea | preference) = 160/360 = 4/9.

Question 5

Events X and Y are independent. P(X) = 0.5 and P(Y) = 0.6. What is P(X and Y)?

Accepted Answer

0.30

Answer

For independent events, P(X and Y) = P(X) × P(Y) = 0.5 × 0.6 = 0.30.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Probability and Conditional Probability 9