A man plays a game of dice in a casino. The man has to pay Rs. 100 for every roll of the dice. If a multiple of 3 turns up, the man doubles his money; else, he forfeits it. In the long run, what is his expected gain or loss per roll of the dice?2
Answers
Given : A man plays a game of dice in a casino.
The man has to pay Rs. 100 for every roll of the dice.
If a multiple of 3 turns up, the man doubles his money; else, he forfeits it.
To Find : In the long run, what is his expected gain or loss per roll of the dice
Solution:
Dice has numbers from 1 to 6
S = { 1 , 2 , 3 ,4 5, 6 }
n(S) = 6
multiples of 3 = { 3 , 6}
Probability to win = 2/6 = 1/3
Probability to forfeit = 1 - 1/3 = 2/3
Net gain of win = 2 * 100 - 100 = 100
Net loss on loss = 100
P(x) x Net Gain xP(x)
1/3 100 100/3
2/3 -100 -200/3
In the long run = ∑xP(x)
= 100/3 - 200/3
= - 100/3
In the long run, he loose 1/3 of his money
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