Question

Two persons A and B play a game by throwing two dice. If the sum of the numbers appeared on the two dice is even, A will get \( \frac{1}{2} \) point and B will get \( \frac{1}{2} \) point. If the sum is odd, A will get one point and B will get no point. The arithmetic mean of the random variable of the number of points of A is

• A. 1/2
• B. 1/4
• C. 1
• D. 3/4

Hint:

Parity of dice sum has equal probability.

Answer 1

The Correct Option is D

Step 1: Probabilities:

Sum Even: \( P(E) = 18/36 = 1/2 \). A gets 1/2 point. Sum Odd: \( P(O) = 18/36 = 1/2 \). A gets 1 point.
Step 2: Expectation:

\( E[A] = (1/2 \times 1/2) + (1 \times 1/2) = 1/4 + 1/2 = 3/4 \).
Step 3: Final Answer:

3/4.