Question

Consider the probability statements regarding events A and B below:

(P(A{ or } B) = 0.3)
(P(A{ and } B) = 0.2)
(P(A|B) = 0.8)
What is (P(B))?

a) 0.4
b) 0.2
c) 0.1
d) 0.6

Answer 1

To find P(B), we use the formula P(B) = (P(A OR B) - P(A|B)) / (1 - P(A|B)). Substituting the given values, we find that P(B) = 0.5. The correct option is a) 0.4.

Step-by-step explanation:

To find P(B), we can use the formula:

P(A OR B) = P(A) + P(B) - P(A AND B)

Using the given information, we have:

P(A OR B) = 0.3

P(A AND B) = 0.2

P(A|B) = 0.8

By rearranging the formula, we can solve for P(B):

P(B) = (P(A OR B) - P(A|B)) / (1 - P(A|B))

P(B) = (0.3 - 0.8) / (1 - 0.8)

P(B) = 0.1 / 0.2

P(B) = 0.5

Therefore, the answer is 0.5, which corresponds to option a) 0.4.