Question

A coin is tossed repeatedly. A and B call alternatively for winning a prize of Rs. $30$. One who calls correctly first wins the prize. A starts the call. Then the expectation of

• A. A is Rs.$10$
• B. B is Rs.$10$
• C. A is Rs. $20$
• D. B is Rs. $20$

Answer 1

Answer: (B), (C)

B is Rs.$10$
A is Rs. $20$

Expectation of A = $\frac{1}{2}\ast 30+(1-\frac{1}{2})\ast (1-\frac{1}{2})\ast \frac{1}{2}\ast 30+(1-\frac{1}{2})\ast (1-\frac{1}{2})\ast (1-\frac{1}{2})\ast (1-\frac{1}{2})\ast \frac{1}{2}\ast 30+...\infty$

Thus, expectation of A = $30\ast \left(\frac{\frac{1}{2}}{1-\frac{1}{4}}\right)=20$

Thus, expectation of B = $30-20=10$