Question
Download Solution PDFA and B are independent events. The odds in favour of A and B are 1:1 and 3:2 respectively. Find the probability that only one of the two events occurs?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Odds in favour of A and B are 1 : 1 and 3 : 2
P(A) = 1/2
P(B) = 3/5
Calculation
The event are independent
⇒ P(A ∩ B) = P(A) × P(B)
⇒ 1/2 × 3/5 = 3/10
The probability that only one of the two events occurs
⇒ P(A) – P(A ∩ B) + [P(B) - P(A ∩ B)]
⇒ (1/2 – 3/10) + [3/5 – 3/10]
⇒ 1/2 + 3/5 – 6/10
∴ The probability that only one of the two events occurs is 1/2
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