MHT CET202616 April 2026Evening ShiftMathematicsProbabilityActual
If E₁ and E₂ are equally likely, mutually exclusive and exhaustive events and P(A|E₁) = 0.2 , P(A|E₂) = 0.3 , then P(E₁|A) equal to...
Options
- A1 5
- B4 5
- C2 3
- D2 5
Correct answer
D. 2 5
Step-by-step solution
Since E₁ and E₂ are equally likely, mutually exclusive and exhaustive events, P(E₁) = P(E₂) = 1 2 . Given P(A|E₁) = 0.2 and P(A|E₂) = 0.3 . Using Bayes' theorem, P(E₁|A) = P(A|E₁)P(E₁) P(A|E₁)P(E₁) + P(A|E₂)P(E₂) P(E₁|A) = 0.2 1 2 0.2 1 2 + 0.3 1 2 P(E₁|A) = 0.2 0.2 + 0.3 = 0.2 0.5 = 2 5 Answer: 2 5