A man wins Rs.100 for getting 5 or 6 on a die throw, loses Rs.50 otherwise.

Question

A man wins Rs.100 for getting 5 or 6 on a die throw, loses Rs.50 otherwise. He throws until he gets a 5 or 6 or a maximum of 3 throws. Find his expected gain/loss.

Accepted Answer

$P(\text{success})=\dfrac13$.

$$E = \frac13(100)+\frac23\cdot\frac13(50)+\left(\frac23\right)^2\left[\frac13(100)-\left(\text{loss term}\right)\right]\cdots$$

Following the source's computation: $E = \dfrac{900+300-1200}{27}=0$.

Solutions · 1