The events A and B have probabilities 0.25 an | vedclass

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(A) Given that, $P(A) = 0.25$ and $P(B) = 0.50$. The probability of both events occurring is $P(A \cap B) = 0.14$. Using the addition rule for probabi

Vedclass · Accepted Answer

$0.39$

Vedclass · Answer

(A) Given that, $P(A) = 0.25$ and $P(B) = 0.50$. The probability of both events occurring is $P(A \cap B) = 0.14$. Using the addition rule for probability, the probability that at least one of the events occurs is: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ $P(A \cup B) = 0.25 + 0.50 - 0.14 = 0.61$. The probability that neither $A$ nor $B$ occurs is given by $P(\bar{A} \cap \bar{B})$, which is equal to $P(\overline{A \cup B})$. $P(\overline{A \cup B}) = 1 - P(A \cup B) = 1 - 0.61 = 0.39$.

The events $A$ and $B$ have probabilities $0.25$ and $0.50$, respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then, the probability that neither $A$ nor $B$ occurs is:

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