Question

Two 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

• A. $0.39$
• B. $0.25$
• C. $0.11$
• D. None of these

Answer 1

Answer: (A)

$P(A \cup B) =P(A)+P(B)-P(A \cap B)$
$=0.25+0.50-0.14 $
$=0.61 $
$ \therefore P\left(A^{\prime}\right.\left.\cap B^{\prime}\right)=P\left((A \cup B)^{\prime}\right)=1-P(A \cup B)$
$=1-0.61=0.39$