Question

The probability of drawing a one-rupee coin from a purse with two compartments, one of which contains 3 fifty paise coins and 2 one-rupee coins and other contains 2 fifty paise coins and 3 one-rupee coins, is

• A. \( 1/2 \)
• B. \( 2/5 \)
• C. \( 1/5 \)
• D. \( 3/5 \)

Hint:

Total probability is the weighted average of probabilities across all possible scenarios or partitions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Use the law of total probability. Let \( C_1, C_2 \) be the choice of compartments and \( R \) be the event of drawing a one-rupee coin.

Step 2: Detailed Explanation:
\( P(C_1) = 1/2, P(C_2) = 1/2 \).
\( P(R|C_1) = 2/5 \).
\( P(R|C_2) = 3/5 \).

\( P(R) = P(R|C_1)P(C_1) + P(R|C_2)P(C_2) \).
\( P(R) = (2/5)(1/2) + (3/5)(1/2) = 1/5 + 3/10 = 2/10 + 3/10 = 5/10 = 1/2 \).

Step 3: Final Answer:
The probability is \( 1/2 \).