Let P (A) = 0.61, P (B) = 0.56, and P (A ∩ B) = 0.46. c. What is the probability that neither A nor B takes place? (Round your answer to 2 decimal places.)

The probability that neither A nor B takes place is 0.29.

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.

0.54

Step-by-step explanation:

P (A∩B) ¹ = 1-0.46 = 0.54