In a betting game wherein the result may be one of the following in one turn: break even, win 5 peso or lose 3 peso. How much will be the amount a player gets after three turns. Let X be the total amount of a player gets after three turns.

Solution:

The probability for each of break even, win 5 peso or lose 3 peso is same as $\dfrac 13$ .

Expected amount a player gets after one turn$=E(X)=0+5\times \dfrac13-3\times\dfrac13=\dfrac23$

Now, expected amount a player gets after three turns$=3E(X)=3\times \dfrac23=2$ peso.