Algebra

Probability

Medium

core

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

0.39

0.61

✅ Correct Option: 3

Given information:

$P(E) = 0.25$

$P(F) = 0.50$

$P(E \cap F) = 0.14$

The probability that neither E nor F occurs can be found using:

$P(\text{neither E nor F}) = 1 - P(\text{at least one of E or F})$

$P(\text{neither E nor F}) = 1 - P(E \cup F)$

To find $P(E \cup F)$ , use the addition rule:

$P(E \cup F) = P(E) + P(F) - P(E \cap F)$

$P(E \cup F) = 0.25 + 0.50 - 0.14$

$P(E \cup F) = 0.61$

Now calculate the probability that neither event occurs:

$P(\text{neither E nor F}) = 1 - P(E \cup F)$

$P(\text{neither E nor F}) = 1 - 0.61$

$P(\text{neither E nor F}) = 0.39$

Therefore, the probability that neither E nor F occurs is 0.39.

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