EJU - Examination for Japanese University Mathematics: Probability and Sets Questions and Answers

Question 1

A bag contains 5 red balls and 3 white balls. If two balls are drawn from the bag at the same time, what is the probability that both balls are red?

Accepted Answer

5/14

Answer

3/14

Answer

5/8

Answer

25/64

Question 2

There are 6 students. In how many ways can a president, vice-president, and treasurer be chosen from this group, assuming no student can hold more than one office?

Accepted Answer

120

Answer

18

Answer

20

Answer

216

Question 3

Let A and B be two sets such that n(A) = 15, n(B) = 20, and n(A ∩ B) = 5. What is the value of n(A ∪ B)?

Accepted Answer

30

Answer

25

Answer

35

Answer

40

Question 4

A single fair die is rolled. What is the probability that the number rolled is a prime number, given that the number is odd?

Accepted Answer

2/3

Answer

1/3

Answer

1/2

Answer

3/5

Question 5

Let U = {x | x is an integer, 1 ≤ x ≤ 10} be the universal set. Let A = {1, 2, 3, 4} and B = {2, 4, 6, 8}. Which of the following represents the set (A ∪ B)ᶜ, the complement of the union of A and B?

Accepted Answer

{5, 7, 9, 10}

Answer

{1, 3, 5, 6, 7, 8, 9, 10}

Answer

{2, 4}

Answer

{1, 3, 6, 8}

Question 6

A coin is flipped 3 times. What is the probability of getting exactly two heads?

Accepted Answer

3/8

Answer

1/8

Answer

1/4

Answer

1/2