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 th a t neither A nor B occurs, is

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

Answer 1

Answer: (A)

0.39

Answer 2

Given, $P(A) =0.25, P(B) = 0.50, P(A \cap B) = 0.14$
$\therefore \, \, \, \, \, P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\, \, \, \, \, \, \, \, \, = 0.25 + 0.50 - 0.14 = 0.61$
Now, $\overline{P(A\cup B)}=1-P(A \cup B)=1-0.61 =0.39$