For this probability experiment a single die is rolled. For Events A, B, and C below, determine which of the following are NOT mutually exclusive.
A: the result is an even number
B: The result is a multiple of 3
C: The result is less than 2
A and B could be 6
A and C - impossible
B and C - impossible
To determine which of the events A, B, and C are NOT mutually exclusive, we need to identify if there are any common outcomes between the events. If there are common outcomes, it means that they are not mutually exclusive.
Event A: The result is an even number.
Outcomes: {2, 4, 6}
Event B: The result is a multiple of 3.
Outcomes: {3, 6}
Event C: The result is less than 2.
Outcomes: {1}
Let's compare the outcomes:
Event A and Event B: The common outcome between Event A and Event B is 6.
Event A and Event C: There are no common outcomes between Event A and Event C.
Event B and Event C: There are no common outcomes between Event B and Event C.
Based on the analysis, the only common outcome exists between Event A (even number) and Event B (multiple of 3), and therefore they are NOT mutually exclusive. Event C (result less than 2) is mutually exclusive with both Event A and Event B since it has no common outcomes.
So, the events that are NOT mutually exclusive are A and B.