Bluebook SAT Test Probability and Conditional Probability 5 — Questions and Answers
Question 1: A two-way table records 400 employees by department and satisfaction level. Satisfied Neutral Dissatisfied Engineering 80 40 30 Marketing 60 60 50 Operations 40 20 20 What is the probability a randomly selected employee is from Marketing and Dissatisfied?
- 1/8 (Correct answer)
- 5/40
- 1/10
- 1/4
Correct answer: 1/8
Marketing & Dissatisfied = 50 out of 400 total; P = 50/400 = 1/8.
Question 2: P(A) = 0.6 and P(A and B) = 0.18. If A and B are independent, what is P(B)?
- 0.30 (Correct answer)
- 0.18
- 0.42
- 0.78
Correct answer: 0.30
Since A and B are independent, P(B) = P(A and B)/P(A) = 0.18/0.6 = 0.30.
Question 3: A box has 3 red, 5 white, and 2 black balls. One ball is drawn and not replaced; then a second is drawn. What is the probability the second ball is red, given the first was white?
- 1/3 (Correct answer)
- 3/10
- 3/9
- 1/4
Correct answer: 1/3
After removing a white ball, 9 balls remain: 3 red; P = 3/9 = 1/3.
Question 4: A game wheel has 4 red, 3 blue, and 1 green section. A player spins twice. What is the probability of getting green both times?
- 1/64 (Correct answer)
- 1/8
- 1/16
- 3/64
Correct answer: 1/64
P(green) = 1/8; for two independent spins, P = (1/8)² = 1/64.
Question 5: In a class of 25 students, the probability that a randomly chosen student plays guitar is 0.32. What is the expected number of guitar players?
- 8 (Correct answer)
- 7
- 6
- 10
Correct answer: 8
Expected value = 25 × 0.32 = 8.
Question 6: The two-way table shows 500 people by exercise frequency and BMI category. Normal BMI High BMI Exercise daily 180 70 Rarely exercise 90 160 What fraction of people with a Normal BMI exercise daily?
- 2/3 (Correct answer)
- 9/10
- 3/5
- 18/27
Correct answer: 2/3
Normal BMI total = 180 + 90 = 270; exercise daily = 180; P = 180/270 = 2/3.
Question 7: A bag has 7 green and 3 yellow tokens. Two tokens are drawn with replacement. What is the probability of drawing one of each color?
- 42/100 (Correct answer)
- 21/50
- 3/10
- 49/100
Correct answer: 42/100
P(green then yellow) + P(yellow then green) = (7/10)(3/10) + (3/10)(7/10) = 42/100 = 21/50.
Bluebook SAT Test Probability and Conditional Probability 5
A two-way table records 400 employees by department and satisfaction level.
Satisfied Neutral Dissatisfied
Engineering 80 40 30
Marketing 60 60 50
Operations 40 20 20
What is the probability a randomly selected employee is from Marketing and Dissatisfied?