Step-by-step explanation:
We have,
P(A) = 0.61, P(B) = 0.56 and P(A ∩ B) = 0.46
To find, the probability that neither A nor B takes place = ?
We know that,
The probability that either A nor B
P ( A ∪ B) = P(A) + P(B) - P(A ∩ B)
∴ P ( A ∪ B) = 0.61 + 0.56 - 0.46
⇒ P ( A ∪ B) = 1.17 - 0.46
⇒ P ( A ∪ B) = 0.71
∴ The probability that neither A nor B = 1 - P ( A ∪ B)
= 0.29
Thus, the probability that neither A nor B takes place is 0.29.
