Answer to Question #199726 in Statistics and Probability for Niju Thomas Rajan

Question

Suppose you roll a pair of dice. Let A be the event that you roll an even number. Let B be the event that you roll an odd number. Which of the following statements is true?

Select one:

a. The intersection of A and B is the empty set ∅.

b. The complement of event B is the set [1, 3, 5, 7, 9, 11].

c. The events A and B are not collectively exhaustive.

d. The events A and B are not mutually exclusive.

Answer 1

a. The intersection of A and B is the empty set ∅. True.

There is no number which is odd and even at the same time.

b. The complement of event B is the set [1, 3, 5, 7, 9, 11]. False.

Since B is the event that you roll an odd number, then the complement of event B is the set [2, 4, 6, 8, 10, 11].

c. The events A and B are not collectively exhaustive. False.

Events A and event B stands to be collectively exhaustive if the union of A and B covers the complete sample space.

$$A\cup B=[2,4,6,8,10,12]\cup[1,3,5,7,9,11]$$

$$=[1,2,3,4,5,6,7,8,9,10,11,12]=S$$

d. The events A and B are not mutually exclusive. False.

A and B are mutually exclusive events if they cannot occur at the same time.

There is no number which is odd and even at the same time.