In a dice game , a player pays a stake of ₹1 for each throw of a die. She receives ₹5, if the die shows a 3, ₹ 2, if the die shows a 1 or 6 and nothing otherwise, then what is the player's expected profit per throw over a long series of throws?

Explanation

Let X is the random variable of profit per throw.

Since, she loss ₹ 1 on getting any of 2, 4 or 5
So, at X=-1 `P(X)=1/6+1/6+1/6=3/6=1/2`
Similarly, at X=1, `P(X)=1/6+1/6=1/3` [If die shows of either 1 or 6]
and at X=4, `P(X)=1/6` [if die shows a 3]
`therefore` Player's expected profit=`E(X)=sumXP(X)`
`=-1xx1/2+1xx1/3+4xx1/6`
`=(-3+2+4)/6=3/6=1/2=₹0.50`