The probabilities of occurance of two events A and B are 0.45 and 0.20 respectively. The probability of their simultaneous occurence is 0.06. The probability that neither A nor B occurs is

0.41

The correct answer is Option (3) → 0.41 **

Given:

$P(A) = 0.45,\ P(B) = 0.20,\ P(A \cap B) = 0.06$

Required: $P(\text{neither A nor B}) = P(\overline{A \cup B}) = 1 - P(A \cup B)$

Now, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$P(A \cup B) = 0.45 + 0.20 - 0.06 = 0.59$

Hence,

$P(\overline{A \cup B}) = 1 - 0.59 = 0.41$

Final Answer:

$0.41$