Final answer:
To find P(B) when events A and B are independent and the probabilities of event A and both events A and B are known, we use the formula P(A and B) = P(A) × P(B). Substituting the values given (P(A) = 0.45 and P(A and B) = 0.34) and solving for P(B), we find P(B) ≈ 0.76.
Step-by-step explanation:
The student is asking how to calculate the probability of event B occurring given that events A and B are independent, and the probability of event A and the probability of both events A and B occurring together are known.
To find P(B), we use the rule that for two independent events A and B, the probability of both events occurring is equal to the product of their individual probabilities: P(A and B) = P(A) × P(B).
We are given that P(A) = 0.45 and P(A and B) = 0.34. We can rearrange the formula to solve for P(B):
P(B) = P(A and B) / P(A)
Substituting the known values we get:
P(B) = 0.34 / 0.45
P(B) = 0.7555555555555555
To two decimal places, P(B) is approximately 0.76.