Prove or disprove via proof that events X and Y can be independent and mutually exclusive if both of their probabilities are greater than 0.

Matias Aguirre

Matias Aguirre

Answered question

2022-07-19

Prove or disprove via proof that events X and Y can be independent and mutually exclusive if both of their probabilities are greater than 0.

Answer & Explanation

Makenna Lin

Makenna Lin

Beginner2022-07-20Added 16 answers

Two events X and Y are independent if and only if P ( X Y ) = P ( X ) P ( Y ). They are mutually exclusive if and only if P ( X Y ) = 0.
In this case, P ( X ) > 0 and P ( Y ) > 0, which means that P ( X ) P ( Y ) > 0. If the events are independent, then P ( X ) P ( Y ) = P ( X Y ) > 0, which would imply that they are not mutually exclusive!
In other words, the events cannot be both independent and mutually exclusive if both of their probabilities are greater than 0.

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