Question

A, B1, B2, B3 are the events in a random experiment. If \( P(B_1)=0.25, P(B_2)=0.30, P(B_3)=0.45 \), \( P(A|B_1)=0.05, P(A|B_2)=0.04, P(A|B_3)=0.03 \), then \( P(B_2|A) = \)

• A. 6/19
• B. 8/19
• C. 12/19
• D. 5/19

Hint:

Use Bayes' Theorem directly.

Answer 1

The Correct Option is A

Step 1: Bayes' Theorem:

\( P(B_2|A) = \frac{P(A|B_2)P(B_2)}{\sum P(A|B_i)P(B_i)} \). Numerator: \( 0.04 \times 0.30 = 0.012 \). Denominator: \( 0.0125 + 0.0120 + 0.0135 = 0.0380 \). Result: \( 0.012 / 0.038 = 12/38 = 6/19 \).
Step 2: Final Answer:

6/19.