Let P(A) = 0.35, P(B) = 0.30, and P(A ∩ B) = 0.17.

a. Are A and B independent events?

multiple choice 1
Yes because P(A | B) = P(A).
Yes because P(A ∩ B) ≠ 0.
No because P(A | B) ≠ P(A).
No because P(A ∩ B) ≠ 0.

b. Are A and B mutually exclusive events?

multiple choice 2
Yes because P(A | B) = P(A).
Yes because P(A ∩ B) ≠ 0.
No because P(A | B) ≠ P(A).
No because P(A ∩ B) ≠ 0.

c. What is the probability that neither A nor B takes place? (Round your answer to 2 decimal places.)

1 answer

c. The probability that neither A nor B takes place can be found using the formula:

P(A' ∩ B') = 1 - P(A ∪ B)

We can find P(A ∪ B) using the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Given that P(A) = 0.35, P(B) = 0.30, and P(A ∩ B) = 0.17, we can substitute these values into the formula:

P(A ∪ B) = 0.35 + 0.30 - 0.17 = 0.48

Now we can find P(A' ∩ B'):

P(A' ∩ B') = 1 - P(A ∪ B) = 1 - 0.48 = 0.52

Therefore, the probability that neither A nor B takes place is 0.52.