Answer:
The probability of winning a jackpot is [tex]P = 0.000003[/tex]
The probability of winning the pick 5 game is [tex]P_a = 0.00001[/tex]
The earning of the lottery organisation if the game were to be runed for no profit is [tex]x =[/tex]$10 000
Step-by-step explanation:
From the question
The sample size is n= 37
The number of selection is [tex]r = 5[/tex]
Now the number of way by which these five selection can be made is mathematically represented as
[tex]\left n} \atop {}} \right.C_r = \frac{n!}{(n-r)!r! }[/tex]
Now substituting values
[tex]\left n} \atop {}} \right.C_r = \frac{37!}{(37-5)!5! }[/tex]
[tex]\left n} \atop {}} \right.C_r = 333333.3[/tex]
Now the probability of winning a jackpot from any of the way of selecting 5 whole number from 37 is mathematically evaluated as
[tex]P = \frac{1}{333333.3}[/tex]
[tex]P = 0.000003[/tex]
Now the number of ways of selecting 5 whole number from 0 to 9 with repetition is mathematically evaluated as
[tex]k = 10^5[/tex]
Now the probability of winning the game is
[tex]P_a = \frac{1}{10^5}[/tex]
[tex]P_a = 0.00001[/tex]
We are told that for a $1 ticket that the pick 5 game returns $50 , 000
Generally the expected value is mathematically represented as
[tex]E(X) = x * P(X =x )[/tex]
In this question the expected value is $1
So
[tex]1 = x * 0.00001[/tex]
So [tex]x = \frac{1}{0.00001}[/tex]
[tex]x =[/tex]$10 000
