Which of the following statements is true? a A. Mutually exclusive events have a joint probability...

Which of the following statements is true?

a A. Mutually exclusive events have a joint probability of 1.

b B. Independent events are mutually exclusive.

c C. Mutually exclusive events cannot occur simultaneously.

d D. Independent events have no effect on the occurrence of one another.

e E. Both C and D are true.

Expert Solution

ans. = e both c and d

a. mutually exclusive means disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0

b. Two events are mutually exclusive if they can't both happen together

Independent events are events where knowledge of the probability of one doesn't change the probability of the other.

there is no correlation between 2 events being mutually exclusive and them being independent.

therefore it is not necessary that : Independent events are mutually exclusive.

c. mutually exclusive means disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0. therefore they will never occur simultaneously.

d. Independent events are events where knowledge of the probability of one doesn't change the probability of the other.

this means that : Independent events have no effect on the occurrence of one another.

P.S. (please upvote if you find the answer satisfactory)

orchestra answered 2 years ago

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