Evaluate P(AUB), if 2P(A) = P(B) = 5/13 and P(A|B) = 2/5
Question:
Evaluate P(AUB), if 2P(A) = P(B) = 5/13 and P(A|B) = 2/5
Solution:
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
Answer:
P(AUB) is 11/13, if 2P(A) = P(B) = 5/13and P(A|B) = 2/5.
Video Solution:
