The probabilities of occurrence of two events E and F are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither E nor F occurs is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.39 **
Given:
$P(E) = 0.25,\ P(F) = 0.50,\ P(E \cap F) = 0.14$
Probability that neither E nor F occurs:
$P(\overline{E \cup F}) = 1 - P(E \cup F)$
Now, $P(E \cup F) = P(E) + P(F) - P(E \cap F)$
$= 0.25 + 0.50 - 0.14 = 0.61$
Therefore,
$P(\overline{E \cup F}) = 1 - 0.61 = 0.39$
Final Answer:
$0.39$