You are told that P(E) = 0.55, P(F) = 0.4, and P(E and F) = 0.28. Are events E and F MUTUALLY EXCLUSIVE? Justify your answer. Be sure to refer to appropriate rules, definitions and properties.
Question
You are told that P(E) = 0.55, P(F) = 0.4, and P(E and F) = 0.28. Are events E and F MUTUALLY EXCLUSIVE? Justify your answer. Be sure to refer to appropriate rules, definitions and properties.
Solution
To determine if events E and F are mutually exclusive, we need to check if the probability of both events occurring simultaneously, P(E and F), is zero.
Mutually exclusive events are defined as events that cannot occur at the same time. Mathematically, if E and F are mutually exclusive, then:
Given the information:
Since is not equal to zero (it is 0.28), events E and F are not mutually exclusive.
Therefore, E and F can occur simultaneously, and they are not mutually exclusive.
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