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

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

Tardigrade Admin · Accepted Answer

P(A ∪ B) =P(A)+P(B)-P(A ∩ B) =0.25+0.50-0.14 =0.61 ∴ P(A prime..∩ B prime)=P((A ∪ B) prime)=1-P(A ∪ B) =1-0.61=0.39

Q. 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

$0.39$

$0.25$

$0.11$

None of these

$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
$= 0.25 + 0.50 - 0.14$
$= 0.61$
$∴ P (A^{'} \cap B^{'}) = P ((A \cup B)^{'}) = 1 - P (A \cup B)$
$= 1 - 0.61 = 0.39$

Q. 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

0.39

0.25

0.11