Evaluate P(AUB), if 2P(A) = P(B) = 5/13 and P(A|B) = 2/5

Question:

Step 1: Find P(A) and P(B)

2P(A) = 5/13

∴ P(A) = 5/26

& P(B) = 5/13

Step 2: Find P(A∩B)

P(A|B) = P(A∩B) / P(B)

∴ 2/5 = P(A∩B) / [5/13]

∴ P(A∩B) = 2/5 x 5/13

∴ P(A∩B) = 2/13

Step 3: Find P(AUB)

P(AUB) = P(A) + P(B) - P(A∩B)

∴ P(AUB) = 5/26 + 5/13 - 2/13

∴ P(AUB) = [5 + 2(5) - 2(2)]/13

∴ P(AUB) = [5 + 10 - 4]/13

∴ P(AUB) = 11/13

P(AUB) is 11/13, if 2P(A) = P(B) = 5/13and P(A|B) = 2/5.