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
Answer & explanation
Correct answer: option 3
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:
$0.41$