Two events A and B have probabilities 0.25 and 0.50 respectively. probability that both A and B occu

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14.Probability

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The 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

$0.904$

D

None of these

(IIT-1980)

Solution

(a) $P({A^c} \cap {B^c}) = 1 – P(A \cup B)$

$ = 1 – [0.25 + 0.5 – 0.14] = 0.39.$

Standard 11

Mathematics

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