Question

question
you have a fair die, with six faces containing the numbers 1,2,3,4,5,6. given events a and b, are the two events mutually exclusive? explain your answer.
event a: rolling a 1 or a 2
event b: rolling an odd number.
select the correct answer below:
yes, the events are mutually exclusive because they have no outcomes in common.
yes, the events are mutually exclusive because ( p(a) ) is not equal to ( p(b) ).
no, the events are not mutually exclusive because they both require rolling the same die.
no, the events are not mutually exclusive because they share the common outcome of 1.

Explanation:

To determine if events \( A \) and \( B \) are mutually exclusive, we check for common outcomes. Event \( A \) includes rolling a 1 or 2 (\(\{1, 2\}\)). Event \( B \) includes rolling an odd number (\(\{1, 3, 5\}\)). The outcome 1 is in both sets, so they share a common outcome. Mutually exclusive events cannot have common outcomes, so these events are not mutually exclusive.

Answer:

D. No, the events are not mutually exclusive because they share the common outcome of 1.