Bluebook SAT Test Probability and Conditional Probability 6 — Questions and Answers
Question 1: A class has 24 students. The probability of any student being absent on a given day is 0.05. What is the expected number of absent students?
- 1.2 (Correct answer)
- 1.0
- 0.5
- 2.4
Correct answer: 1.2
E = n × p = 24 × 0.05 = 1.2.
Question 2: The two-way table shows 200 voters by party and stance on a bill. Favor Oppose Democrat 70 30 Republican 20 80 Given that a voter favors the bill, what is the probability the voter is a Republican?
- 2/9 (Correct answer)
- 1/5
- 4/9
- 2/11
Correct answer: 2/9
Total favoring = 70 + 20 = 90; Republicans favoring = 20; P = 20/90 = 2/9.
Question 3: Cards numbered 1 through 20 are shuffled. One card is drawn at random. What is the probability the card shows a multiple of 3 or a multiple of 5?
- 2/5 (Correct answer)
- 1/2
- 9/20
- 7/20
Correct answer: 2/5
Multiples of 3: {3,6,9,12,15,18} = 6; multiples of 5: {5,10,15,20} = 4; overlap {15} = 1; union = 9; P = 9/20.
Question 4: A bag has 5 red and 5 blue chips. Two chips are drawn without replacement. What is the probability both are the same color?
- 4/9 (Correct answer)
- 1/2
- 2/5
- 5/9
Correct answer: 4/9
P(RR) = (5/10)(4/9) = 20/90; P(BB) = (5/10)(4/9) = 20/90; total = 40/90 = 4/9.
Question 5: A company's hiring data shows: 40% of applicants pass the written test and, of those, 30% pass the interview. What percent of all applicants get hired?
- 12% (Correct answer)
- 30%
- 40%
- 70%
Correct answer: 12%
P(pass written and interview) = 0.40 × 0.30 = 0.12 = 12%.
Question 6: The two-way table shows 300 students by study method and test result. Pass Fail Study group 110 40 Study alone 90 60 What is the probability a student who failed studied alone?
- 3/5 (Correct answer)
- 1/3
- 2/5
- 3/10
Correct answer: 3/5
Total failing = 40 + 60 = 100; studied alone and failed = 60; P = 60/100 = 3/5.
Question 7: A number is selected at random from 1 to 50. What is the probability it is divisible by both 4 and 6?
- 2/25 (Correct answer)
- 1/10
- 1/12
- 3/50
Correct answer: 2/25
LCM(4,6) = 12; multiples of 12 up to 50: {12, 24, 36, 48} = 4; P = 4/50 = 2/25.
Bluebook SAT Test Probability and Conditional Probability 6
A class has 24 students.
The probability of any student being absent on a given day is 0.05.
What is the expected number of absent students?