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?

Options

A. 0.5
B. 0.2
C. 0.7
D. 0.9

Answer

A

Explanation

Let X be the money won in one throw
Money lost in 1 throw = र1
Also, probability of getting `3=1/6`
probability of getting 1 or 6
`rArr" "1/6+1/6=2/6`
probability of getting any other number i.e. 2 or 4 or 5
`=1/6+1/6+1/6=3/6`
Then probability distribution is
The expected money that player can won
`E(X)=5/6+4/6+0=9/6=र1.5`
Then, players expected profit =र 1.5-र 1=र 0.50