Question

If \(E_1\) and \(E_2\) are equally likely, mutually exclusive and exhaustive events and \(P(A|E_1) = 0.2\), \(P(A|E_2) = 0.3\), then \(P(E_1|A)\) equal to...

• A. \(\frac{1}{5}\)
• B. \(\frac{4}{5}\)
• C. \(\frac{2}{3}\)
• D. \(\frac{2}{5}\)

Hint:

Apply Bayes theorem with equal priors, so the priors cancel.

Answer 1

The Correct Option is D

Step 1: Equal priors
With equal priors, the posterior is proportional to the likelihood: $0.2 : 0.3 = 2 : 3$.

Step 2: Normalise
$P(E_1|A) = \frac{2}{2+3} = \frac25$. Option (D).

Final Answer:
2/5. \[ \boxed{\text{(D)}\ \frac25} \]