(D) Given: $P(A) = 0.25$,$P(B) = 0.50$,and $P(A \cap B) = 0.12$. First,we find the probability of the union of the two events using the addition theor

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(D) Given: $P(A) = 0.25$,$P(B) = 0.50$,and $P(A \cap B) = 0.12$. First,we find the probability of the union of the two events using the addition theorem: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ $P(A \cup B) = 0.25 + 0.50 - 0.12 = 0.63$. We need to find the probability that neither event occurs,which is $P(A' \cap B')$. By De Morgan's Law,$P(A' \cap B') = P((A \cup B)') = 1 - P(A \cup B)$. Therefore,$P(A' \cap B') = 1 - 0.63 = 0.37$.

Class 11 Mathematics Probability Odds in favor and odds against, Addition theorem on probability

Medium

The probabilities of two events $A$ and $B$ occurring are $0.25$ and $0.50$ respectively. The probability of both events occurring simultaneously is $0.12$. Find the probability that neither event occurs.

A
$0.13$
B
$0.38$
C
$0.63$
D
$0.37$

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Odds in favor and odds against, Addition theorem on probability

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The probabilities of two events $A$ and $B$ occurring are $0.25$ and $0.50$ respectively. The probability of both events occurring simultaneously is $0.12$. Find the probability that neither event occurs.

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