In a lottery game, the jackpot is won by selecting five different whole numbers

Question

In a lottery game, the jackpot is won by selecting five different whole numbers from 1 through 36 and getting the same five numbers (in any order) that are later drawn. In the Pick 4 game, you win a straight by selecting four digits (with repetition allowed), each one from 0 to 9, and getting the same four digits in the exact order they are later drawn. The Pick 4 game returns $5,000 for a winning $1 ticket. Complete parts (a) through (c) below. a. In a lottery game, the jackpot is won by selecting five different whole numbers from 1 through 36 and getting the same five numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game? P(winning a jackpot in this game) = (Type an integer or a simplified fraction.) b. In the Pick 4 game, you win a straight bet by selecting four digits (with repetition allowed) each one from 0 to 9, and getting the same four digits in the order they are later drawn. What is the probability of this game? P(winning the Pick 4 game) = (Type an integer or a simplified fraction.) c. The Pick game returns $5,000 for a winning $1 ticket. What should be the return if the lottery organization were to run this game for no profit? $ (Type a whole number.)

Explanation / Answer

A) Number of ways in which 5 numbers can be selected from the lottery game = 36C5 = 376992

So, probability of winning a jackpot in this game = 1/376,992

B) Number of possible options in pick 4 game = 104= 10,000

P(winning the pick 4 game) = 1/10000

C) Amount earned from pick 4 game = $1 x 10,000 = $10,000

If there is no profit, the return must be $10,000

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