In roulette, Fig. 32.2, the wheel has 13 numbers 0,1,2,….,12 marked on equally spaced slots. A player sets ₹10 on a given number. He receives ₹100 from the organizer of the game if the ball comes to rest in this slot; otherwise he gets nothing. If X denotes the player’s net gain/loss, find E (X).

As player sets Rs 10 on a number ,if he wins he get Rs 100


∴ his profit is Rs 90.


If he loses, he suffers a loss of Rs 10


He gets a profit when ball comes to rest in his selected slot.


Total possible outcome = 13


Favourable outcomes = 1


∴ probability of getting profit = 1/13


And probability of loss = 12/13


If X is the random variable denoting gain and loss of player


∴ X can take values 90 and -10


P(X=90) = 1/13


And P(X=-10) = 12/13


Now we have pi and xi.


Let’s proceed to find mean


Mean of any probability distribution is given by Mean = ∑xipi


∴ first we need to find the products i.e. pixi and add them to get mean


Following table representing probability distribution gives the required products :



E(X) = Mean =


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