Question 48

Mathematics Probability Hard

The probability 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 occur is

(A) 0.61
(B) 0.11
(C) 0.39
(D) 0.89
View Dynamic Solution & Explanation
Correct Solution: Option C

Step-by-step Solution:

\[ P(E \cup F) = P(E) + P(F) - P(E \cap F) \] \[ \Rightarrow P(E \cup F) = 0.25 + 0.50 - 0.14 = 0.61 \] Now, the probability that neither \(E\) nor \(F\) occurs is: \[ 1 - P(E \cup F) = 1 - 0.61 = 0.39 \]