Q1- In a dice game, a player pays a stake of Re1 for each throw of a die. Shereceives Rs 5 if the die shows a 3, Rs 2 if the die shows a 1 or 6, and nothingotherwise. What is the players expected profit per throw over a long series ofthrows?

Here the person get 5Rs when the dice show 3.
The probability of getting 3 is 1/6

And she get 2rs on getting 1 or 6
So the probability of getting 1 or 6 is 2/6 = 1/3

And she will get zero on getting rest, which is 4,5,2
The probability of that is 3/6 = 1/2

Hence total money earned = 1/6* 5 + 1/3 * 2 + 1/2*0 = 9/6Rs

And she spent 1Rs/stake
So toatl profit = 9/6 -1 = 3/6 = 0.5Rs

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