# Specify the probability distribution of X in the following case:In a charity lottery, 100 tickets are sold for $10 each. One first prize of $200, and one second prize of $100 are to be awarded....

Specify the probability distribution of X in the following case:

In a charity lottery, 100 tickets are sold for $10 each. One first prize of $200, and one second prize of $100 are to be awarded. Consider a person who buys two tickets, and let X=the net amount won by the person.

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### 1 Answer

In the charity lottery, 100 tickets worth $10 each are sold. 2 tickets are chosen as winners with the first prize of $200 and the second prize of $100. The probability distribution of the net amount X made by a person who buys 2 tickets is required.

The person can not win any of the prizes. That would make the net amount won -$20. If the person wins only the first prize, the net amount won is $180. If the person only wins the second prize, the net amount won is $80 and if the person wins both the prizes the net amount won is $280.

The probability of X = -$20 is 98*97/100*99 = 4753/4950

The probability of X = $80 is 2*(1/100)*(98/99) = 98/4950

The probability of X = $180 is 2*(1/100)*(98/99) = 98/4950

The probability of X = $280 is (1/100)*(1/99) = 1/4950

It can be seen that `4753/4950+98/4950+98/4950+1/4950 = 1`

**The required probability distribution of the person's net gain X is:**

**-$20 : `4753/4950` , $80 : `98/4950` , $180 : `98/4950` , $280 : `1/4950` **