Question

In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 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.

Answer 1

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:

He can win around Rs 1.45