In a game, a man wins ₹5 for getting a number greater than 4 and loses ₹1 otherwise, when a fair die is thrown. The man decided to throw a die thrice but to quits as and when he gets a number than 4. Find the expected value of amount he wins/lose.
We are asked to find the expected amount he wins or lose i.e we have to find the mean of probability distribution of random variable X denoting the win/loss.
As he decided to throw the dice thrice but to quit at the instant he loses
∴ if he wins in all throw he can make earning of Rs 15
If he wins in first two throw and lose in last, he earns Rs (10-1) = Rs 9
If he wins in first throw and then loses ,he earns = Rs 4
If he loses in first throw itself, he earns Rs = -1
Thus X can take values -1,4,9 and 15
P(getting a number greater than 4 in a throw of die) = 2/6 = 1/3
P(getting a number not greater than 4 in a throw of die) = 4/6 = 2/3
P(X=-1) = P(getting number less than or equal to 4) = 2/3
P(X=4) = P(getting > 4) x P(getting ≤ 4) = 
P(X=9) = P(getting > 4) x P(getting > 4) x P(getting ≤ 4) = 
P(X=15) = P(getting > 4) x P(getting > 4) x P(getting > 4) = 
So, Probability distribution is given below:
∵ Mean = ∑xipi
Mean = 
He can win around Rs 1.45