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

Question

Dr. Abubacker · Accepted Answer

(a)
$P(A) = 0.25,\ P(B) = 0.50,\ P(A \cap B) = 0.14$
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$= 0.25 + 0.50 - 0.14 = 0.61$
$	herefore P\left( \overline{A} \cap \overline{B} ight) = P(\overline{A \cup B})$=$1 - \ P(A \cup B)$
$= 1 - 0.61 = 0.39$

Q. Two events $A\ and\ B$ have probability 0.25 and 0.50 respectively. The probability that both $A\ and\ B$ occur simultaneously is 0.14. Then, the probability that neither $A\ nor\ B$ occur, is

Explanation

Reviewed by Dr. Abubacker

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