Question

in a states pick 3 lottery game you pay $1.26 to select a sequence of three digits, such as 688. if you select the same sequence of three digits that are drawn, you win and collect $402.03a. how many different selections are possible?b. what is the probability of winning?c. if you win what is your net profit?d. find the expected value (please show work for this part)e. if you bet $1.49 in a certain states pick 4 game, the expected value is -$1.01. which bet is better, a $1.49 bet in the pick 3 game or a $1.49 bet in the pick 4 game?

Answer 1

Answer and explanation:

Given : In a states pick 3 lottery game you pay $1.26 to select a sequence of three digits, such as 688. if you select the same sequence of three digits that are drawn, you win and collect $402.03.

To find :

a. How many different selections are possible?

Sequence of three digits that are drawn.

So, Numbers can range from 000 to 999.

i.e.
`10^3=1000`

There are 1000 possible solutions.

b. What is the probability of winning?

The probability of winning is given by,

`P=(1)/(1000)=0.001`

c. If you win what is your net profit?

If you win, profit = 402.03 - 1.26 = $400.77

d. Find the expected value ?

The probability of winning is
`(1)/(1000)` and you will get $400.77 if you win and probability of losing is
`(999)/(1000)` and you will have to pay $1.26 if you loose.

Expected value is given by
`E(X)=X* P(X)`

i.e.
`E(X)=400.77* ((1)/(1000)) - (1.26)* ((999)/(1000))`

`E(X)=−0.85797`

e. If you bet $1.49 in a certain states pick 4 game, the expected value is -$1.01. which bet is better, a $1.49 bet in the pick 3 game or a $1.49 bet in the pick 4 game?

States pick 3 is better, since expected value in states pick is more negative compared to that in States pick 3.