4.6 10)In a lottery game, the jackpot is won by selecting seven different whole

Question

4.6
10)In a lottery game, the jackpot is won by selecting seven different whole numbers from 1 through 40 and getting the same seven numbers (in any order) that are later drawn. 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 exact order they are later drawn. The Pick 4 game returns $5,000for a winning $1 ticket. Complete parts (a) through (c) below.

a. In a lottery game, the jackpot is won by selecting seven different whole numbers from 1 through 40 and getting the same seven
numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game?

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 exact order they are later drawn. What is the probability of winning this game?
P(winning the Pick 4game)___________

(Type an integer or a simplified fraction.)

c. The Pick 4 game returns 5000 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.)

13) Winning the jackpot in a particular lottery requires that you select the correct threenumbers between 1 and 40 and, in a separate drawing, you must also select the correct single number between 1 and 53. Find the probability of winning the jackpot.

The probability of winning the jackpot is_________

(Please answer both questions all parts)

Explanation / Answer

a)

Since we have to choose 5 different numbers from 1 to 40, and since the order does not matter, so combination rule must be used. Possible 7 numbers out of 40 numbers is:

40C7 = 18,643,560

Out of 18,643,560 ways, there is only one way corresponding to Jackpot, so, the probability of jackpot is:

P(Jackpot) = 1/ 18,643,560

b) There are 10 numbers (0 to 9) available for each selection. Therefore, total possible ways are 10*10*10*10=10,000.

The probability of winning the game is:

P(Winning the game) = 1/10,000

c) P(Winning the game) = 1/10,000

and P(not winning the game) = 9999/10,000

Odds against winning = 9999:1

Since lottery organization were to run this game for no profit, so pay off odds will be:

Pay off odds = net profit : actual bet = 9999:1

That is, for $1 bet, lottery organization has to pay $10,000. hence it should return $10,000.

#13

Using rule shown in previous poblem part a, The probability of winning Jackpot is:

P(Jackpot) = 1/(40C3 * 53C1) =  1/(9880 * 53) = 1/523,640

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