Respuesta :
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. [tex]10^3=1000[/tex]
There are 1000 possible solutions.
b. What is the probability of winning?
The probability of winning is given by,
[tex]P=\frac{1}{1000}=0.001[/tex]
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 [tex]\frac{1}{1000}[/tex] and you will get $400.77 if you win and probability of losing is [tex]\frac{999}{1000}[/tex] and you will have to pay $1.26 if you loose.
Expected value is given by [tex]E(X)=X\times P(X)[/tex]
i.e. [tex]E(X)=400.77\times (\frac{1}{1000}) - (1.26)\times (\frac{999}{1000})[/tex]
[tex]E(X)=−0.85797[/tex]
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.
