Bluebook SAT Test Probability and Conditional Probability 4 — Questions and Answers
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?
- 1/2 (Correct answer)
- 1/3
- 2/3
- 1/4
Correct answer: 1/2
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?
- 2/5 (Correct answer)
- 1/3
- 4/9
- 2/9
Correct answer: 2/5
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?
- No, because P(A and B) = 0.2 ≠ 0 (Correct answer)
- Yes, because P(A and B) = 0
- Cannot be determined
- Yes, because P(A) + P(B) = 0.9
Correct answer: No, because P(A and B) = 0.2 ≠ 0
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?
- 3/10 (Correct answer)
- 2/5
- 12/50
- 1/4
Correct answer: 3/10
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?
- 1/3 (Correct answer)
- 1/6
- 1/2
- 2/3
Correct answer: 1/3
Odd outcomes are {1, 3, 5}; among these, only 3 is favorable; P = 1/3.
Question 6: A student randomly selects one question from a test bank of 40 questions: 16 algebra, 14 geometry, and 10 statistics. What is the probability of selecting an algebra or statistics question?
- 13/20 (Correct answer)
- 2/5
- 7/20
- 3/5
Correct answer: 13/20
Algebra + statistics = 16 + 10 = 26 out of 40; P = 26/40 = 13/20.
Question 7: A school surveys 100 students. 55 like math, 45 like English, and 20 like both. What is the probability a randomly selected student likes exactly one subject?
- 3/5 (Correct answer)
- 4/5
- 1/4
- 2/5
Correct answer: 3/5
Exactly one = (55 − 20) + (45 − 20) = 35 + 25 = 60; P = 60/100 = 3/5.
Bluebook SAT Test Probability and Conditional Probability 4
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?