(A) The probability that neither $A$ nor $B$ occurs is given by $P(A' \cap B') = 1 - P(A \cup B)$.Since $A$ and $B$ are mutually exclusive events,$P(A

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(A) The probability that neither $A$ nor $B$ occurs is given by $P(A' \cap B') = 1 - P(A \cup B)$.Since $A$ and $B$ are mutually exclusive events,$P(A \cap B) = 0$.Therefore,$P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.5 + 0.3 - 0 = 0.8$.Now,the required probability is $1 - P(A \cup B) = 1 - 0.8 = 0.2$.

Competitive Quantitative Aptitude Probability Probability

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The probability of an event $A$ occurring is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events,find the probability that neither $A$ nor $B$ occurs.

A
$0.2$
B
$0.8$
C
$0.6$
D
None of these

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The probability of an event $A$ occurring is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events,find the probability that neither $A$ nor $B$ occurs.

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