Question

Ram and shyam throw with one dice for a prize of $Rs.88$ which is to be won by the player who throws $1$ first. If ram starts, then mathematical expectation for shyam is

• A. $Rs.32$
• B. $Rs.40$
• C. $Rs.48$
• D. None of these

Answer 1

Answer: (B)

$Rs.40$

Probability of winning of Shyam
$=\frac{5}{6}\times \frac{1}{6}+\frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}\times \frac{1}{6}+...=\frac{5}{36}[1+\frac{25}{36}+{\left(\frac{25}{36}\right)}^2+...]$
$=\frac{5}{36}\times \frac{1}{1-\frac{25}{36}}=\frac{5}{36}\times \frac{36}{11}=\frac{5}{11}$