Question

A and B throw one dice for a stake of Rs.11, which is to be won by the player who first throws a six. The game ends when the stake is won by A or B. If A has the first throw, what are their respective expectations?

• A. 5 and 6
• B. 6 and 5
• C. 11 and 0
• D. 10 and 1

Hint:

Since A throws first, his winning chance is 6/11 versus B's 5/11; multiply each by the Rs.11 stake.

Answer 1

The Correct Option is B

Step 1: Set up recursive equation.
Let p be probability of the player about to throw winning. p = 1/6 + 5/6(1-p)

Step 2: Solve.
p = 1 - 5p/6 => 11p/6 = 1 => p = 6/11

Step 3: Expectations.
E(A)=6/11x11=6, E(B)=5/11x11=5

Final Answer: A's expectation is Rs.6 and B's expectation is Rs.5.