Question

In a lottery​ game, the jackpot is won by selecting five different whole numbers from 1 through 37 and getting the same five numbers​ (in any​ order) that are later drawn. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. Complete parts​ (a) through​ (c) below:a. What is the probability of winning a jackpot in this​ game? ​P(winning a jackpot in this ​game)= ________b. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. What is the probability of winning this​ game? ​P(winning the Pick 55​game)= ______________c. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. What should be the return if the lottery organization were to run this game for no​ profit? ​

Answer 1

The probability of winning a jackpot is
`P = 0.000003`

The probability of winning the pick 5 game is
`P_a = 0.00001`

The earning of the lottery organisation if the game were to be runed for no profit is
`x =`$10 000

Explanation:

From the question

The sample size is n= 37

The number of selection is
`r = 5`

Now the number of way by which these five selection can be made is mathematically represented as

`\left n} \atop {}} \right.C_r = (n!)/((n-r)!r! )`

Now substituting values

`\left n} \atop {}} \right.C_r = (37!)/((37-5)!5! )`

`\left n} \atop {}} \right.C_r = 333333.3`

Now the probability of winning a jackpot from any of the way of selecting 5 whole number from 37 is mathematically evaluated as

`P = (1)/(333333.3)`

`P = 0.000003`

Now the number of ways of selecting 5 whole number from 0 to 9 with repetition is mathematically evaluated as

`k = 10^5`

Now the probability of winning the game is

`P_a = (1)/(10^5)`

`P_a = 0.00001`

We are told that for a $1 ticket that the pick 5 game returns $50 , 000

Generally the expected value is mathematically represented as

`E(X) = x * P(X =x )`

In this question the expected value is $1

So

`1 = x * 0.00001`

So
`x = (1)/(0.00001)`

`x =`$10 000