Bluebook SAT Test Probability and Conditional Probability 1

Question 1

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it is NOT green?

Accepted Answer

4/5

Answer

There are 8 non-green marbles out of 10 total, so P(not green) = 8/10 = 4/5.

Question 2

A survey of 200 students found that 120 play sports and 80 play an instrument. If 40 students do both, how many students do neither?

Accepted Answer

40

Answer

Using inclusion-exclusion: sports or instrument = 120 + 80 − 40 = 160, so neither = 200 − 160 = 40.

Question 3

The two-way table shows pet ownership among 150 households.

Cat  No Cat
Dog       30     45
No Dog    25     50

Given that a household has a dog, what is the probability it also has a cat?

Accepted Answer

2/5

Answer

There are 30 + 45 = 75 dog households; 30 have both, so P(cat | dog) = 30/75 = 2/5.

Question 4

A standard die is rolled twice. What is the probability of getting a 4 on the first roll and a number greater than 2 on the second roll?

Accepted Answer

1/9

Answer

P(4) = 1/6 and P(>2) = 4/6 = 2/3; since independent, multiply: (1/6)(2/3) = 2/18 = 1/9.

Question 5

In a class of 30 students, 18 passed the math test and 12 passed the science test. If 6 students passed both, what is the probability that a randomly selected student passed at least one test?

Accepted Answer

4/5

Answer

Students passing at least one = 18 + 12 − 6 = 24; P = 24/30 = 4/5.

Bluebook SAT Practice Test Practice Test

Bluebook SAT Practice Test Practice Test

Bluebook SAT Test Probability and Conditional Probability 1