Question

If P(A) = 0.4, P(B|A) = 0.25, P(A ∪ B) = 0.67, find P(B).

a) 0.1
b) 0.37
c) 0.57
d) 0.65

Answer 1

To find P(B), use the formula for conditional probability and the given information.

Step-by-step explanation:

To find P(B), we can use the formula for conditional probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Given that P(A) = 0.4, P(B|A) = 0.25, and P(A ∪ B) = 0.67, we can rearrange the formula to find P(B):

P(B) = P(A ∪ B) - P(A) + P(A ∩ B)

= 0.67 - 0.4 + (0.25)(0.4)

= 0.57.

Therefore, the probability of event B occurring is 0.57.