Question

If P(A∪B) = 0.7, P(A) = 0.4, and P(A∩B) = 0.35, find P(B). Assume that A and B are events.

P(B)=

Answer 1

The probability of event B (P(B)) is calculated using the formula P(A ∪ B) = P(A) + P(B) − P(A ∩ B). By substituting the known values and solving for P(B), we find that P(B) is 0.65.

Step-by-step explanation:

The student's question is asking how to find the probability of event B (P(B)) given that we already know the probability of the union of events A and B (P(A∪B)), the probability of event A (P(A)), and the probability of the intersection of events A and B (P(A∩B)). To solve for P(B), you can utilize the formula for the probability of the union of two events:

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Plugging in the known values, we get:

0.7 = 0.4 + P(B) - 0.35

Now, to find P(B), we simply rearrange the equation and solve for P(B):

P(B) = 0.7 + 0.35 - 0.4

P(B) = 1.05 - 0.4

P(B) = 0.65

Therefore, the probability of event B is 0.65.