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If P(A) = 0.65, P(B) = 0.76 and P(A union B) = 0.80, then P(A intersect B) is (blank).

Question:

If {eq}P(A) = 0.65, \; P(B) = 0.76 {/eq} and {eq}P(A \cup B) = 0.80, {/eq} then {eq}P(A \cap B) {/eq} is {eq}\rule{1cm}{0.15mm} {/eq}.

Mutually Exclusive Events:

Two or more events are said to be mutually exclusive, if they can not occur at the same time. They are also referred to as disjoint events.

Answer and Explanation:

Mutually exclusive events are described by the following equation:

{eq}\begin{align*} P(A\cap B)&=P(A)+P(B)-P(A\cup B)\\&=0.65+0.76-0.80\\&=0.61 \end{align*} {/eq}


Learn more about this topic:

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Mutually Exclusive in Statistics: Definition, Formula & Examples

from High School Algebra II: Help and Review

Chapter 25 / Lesson 8
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