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Question
If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find P(only B)
Solution
Given P(A) = 0.35
P(A and B) = P(A ∩ B) = 0.15
P(A or B) = P(A ∪ B) = 0.85
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
0.85 = 0.35 + P(B) – 0.15
0.85 + 0.15 – 0.35 = P(B)
P(B) = 1 – 0.35
P(B) = 0.65
P(only B) = `"P"(bar"A" ∩ "B")`
= P(B) – P(A ∩ B)
= 0.65 – 0.15
P(only B) = 0.50
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