$A$ and $B$ are mutually exclusive events. [tex]
\begin{array}{l}
P(A)=0.50 \\
P(B)=0.20
\end{array}
[/tex] What is $P(A$ and $B)$?
Answer (1)
Mutually exclusive events cannot occur at the same time.
The probability of two mutually exclusive events both occurring is 0.
Therefore, P ( A e wl in e an d e wl in e B ) = 0 .
The final answer is 0 .
Explanation
Understanding Mutually Exclusive Events We are given that events A and B are mutually exclusive, which means they cannot occur at the same time. In probability terms, this means that the probability of both A and B occurring together is 0.
Applying the Definition Since A and B are mutually exclusive, the probability of A and B occurring together, denoted as P ( A e wl in e an d e wl in e B ) , is 0.
Final Answer Therefore, P ( A e wl in e an d e wl in e B ) = 0 .
Examples
Consider a game where you can either win a prize (event A) or lose (event B), but not both at the same time. If the probability of winning is 0.50 and the probability of losing is 0.20, the probability of both winning and losing simultaneously is 0, because these events are mutually exclusive. This concept is useful in risk assessment and decision-making, where understanding mutually exclusive outcomes helps in evaluating possible scenarios and their likelihood.
