Question

Vasant and Jothi play a game with a coin. Vasant stakes INR 1 and throws the coin four times. If he throws four heads, he gets his stake and INR3 from Jothi. If he throws only three heads and they are consecutive, he gets his stake and INR 2 from Jothi. If he throws only two heads and they are consecutive, he gets his stake and INR 1 from Jothi. In all other cases Jothi takes the stake money. Find the expectation of Vasant's gain.

• A. \( -\frac{5}{8} \)
• B. 0
• C. 1
• D. \( \frac{5}{8} \)

Hint:

For expected gain problems, list each possible gain with its probability and then use \(E(X)=\sum x_i p_i\).

Answer 1

The Correct Option is B