In a game, you pay $1 to select a sequence of four digits, such as 0112. You win

Question

In a game, you pay $1 to select a sequence of four digits, such as 0112. You win when the selected sequence of four digits matches with a fixed sequence of four digits exactly (same digits in same order). The winning prize is $5000. (a) If you buy only one ticket and win, what is your net gain, namely the amount you win subtract the amount you pay? (b) If you buy one ticket, what is the probability of winning? (c) Let random variable x be the net gain of purchasing one ticket. Construct a table describing the probability distribution corresponding to all possible values of x.

Explanation / Answer

a)net gain =prize money-ticket cost =5000-1=4999

b)total number of 4 digit sequence =10*10*10*10 =10000

hence probability of winning =1/10000 =0.0001

c)here winning amount x=4999 and corresponding probabilty =P(X=4999)=0.0001

and losing amount =x=-1 and corresponding probability =1-0.0001=0.9999

hence

please reply

x P(x) -1 0.9999 4999 0.0001

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