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11.In a lottery​ game, the jackpot is won by selecting six different whole numbers from 1...

11.In a lottery​ game, the jackpot is won by selecting six different whole numbers from 1 through 38 and getting the same six numbers​ (in any​ order) that are later drawn. In the Pick 3 ​game, you win a straight bet by selecting three digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same three digits in the exact order they are later drawn. The Pick 3 game returns $500 for a winning​ $1 ticket. Complete parts​ (a) through​ (c) below.

a. In a lottery​ game, the jackpot is won by selecting six different whole numbers from 1 through 38 and getting the same six 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 3 ​game, you win a straight bet by selecting three digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same three digits in the exact order they are later drawn. What is the probability of winning this​ game?

​P(winning the Pick 3 ​game)=_________

​

c. The Pick 3 game returns ​$500 for a winning​ $1 ticket. What should be the return if the lottery organization were to run this game for no​ profit?

$___________

math   Statistics-And-Probability   
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Answer #1

38 a. The order of the balls doesnt matter, and so there are() po possible outcomes 38 38! - 2760681 6 6! (38 6)! the probability of winning a jackpot in this game would be 2760681 We can get to this probability by another route: ㄨㄧㄨㄧㄨㄧㄨㄧㄨ 38 3736 35 34 33 There are 38 balls and 6 match one of the winners initially (6/38). Were sampling without replacement, so this leaves 37 balls, 5 of which are winners, since we have already drawn the 1 winner (5/37). The other terms (4/36, 3/35, 2/34 and 1/33) are added similarly b. The number of ways of selecting the first digit 10 (0-9 digits) The number of ways of selecting the second digit with repetition allowed 10 The number of ways of selecting the third digit with repetition allowed 10 Total number of ways of selecting three digits (i.e. 0-9) with repetition allowed is given as Totalnumber of ways 10x10x10 1000 The probability of winning this game would be 1000 c. For winning $1 ticket they will have to give $500, that means they will lose $499 which has chance 1/1000 from part b, probability of not winning lottery would be 1-1/1000- 999/1000, in this case they will get $1 E(x)- x * P(x) 999_0.5 Expected profit499 +1000 1000 The expected return would be $0.5

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