Answer :

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


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