If $P(A) = \frac{3}{5}$ and $P(B) = \frac{1}{5}$, find $P(A \cup B)$ if $A$ and $B$ are mutually exclusive events.
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Question

If $P(A) = \frac{3}{5}$ and $P(B) = \frac{1}{5}$, find $P(A \cup B)$ if $A$ and $B$ are mutually exclusive events.

Accepted Answer

For mutually exclusive events, $P(A \cap B) = 0$. The addition theorem of probability states that $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. Substituting the given values, we get $P(A \cup B) = \frac{3}{5} + \frac{1}{5} - 0 = \frac{4}{5}$. Thus, the correct option is $\frac{4}{5}$.

Probability

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