Answer to Question #254428 in Statistics and Probability for Rahima

Question

4- Event A

: Rolling an even number on a fair die.

Event B

: Rolling a 6

 on a fair die.

Event C

: Rolling an odd number on a fair die.

Given the three events, which of the following statements is true? Select all that apply.

Select all that apply:

• Event A
•  and Event B
•  are mutually exclusive.
  
• Event B
•  and Event C
•  are mutually exclusive.
  
• Event A
•  and Event C
•  are not mutually exclusive.
  
• Event A
•  and Event C
•  are mutually exclusive.

5- Suppose A

and B

are mutually exclusive events, and that P(A)=0.13

and P(B)=0.85

. Find P(A OR B)

Answer 1

Two events are mutually exclusive when they cannot happen simultaneously.

Event A - Rolling an even number on a fair die.

Event B - Rolling a 6 on a fair die.

Event C - Rolling an odd number on a fair die.

So, the sets that satisfy events are as follows:

A = {2, 4, 6}

B - {6}

C - {1,3,5}

• Event A
•  and Event B
•  are mutually exclusive.

This statement is false because the number six satisfies both events

• Event B
•  and Event C
•  are mutually exclusive.

This statement is true because there is no number that satisfies both events (their intersection is an empty set)

• Event A
•  and Event C
•  are not mutually exclusive.

This statement is false because there is no number that satisfies both events (their intersection is an empty set), so they are mutually exclusive

• Event A
•  and Event C
•  are mutually exclusive

This statement is an opposite to the previous one, so it is true.

Suppose A and B are mutually exclusive events, and that P(A)=0.13

and P(B)=0.85

Find P(A OR B)

P(A OR B) = P(A) + P(B) - P(A and B) = 0.13 + 0.85 - 0 = 0.98