Respuesta :
Answer:
The expected winnings for a person buying 1 ticket is -0.2.
Step-by-step explanation:
Given : A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each. If 20000 tickets are sold at 25 cents each, find the expected winnings for a person buying 1 ticket.
To find : What are the expected winnings?
Solution :
There are one first prize, 2 second prize and 20 third prizes.
Probability of getting first prize is [tex]\frac{1}{20000}[/tex]
Probability of getting second prize is [tex]\frac{2}{20000}[/tex]
Probability of getting third prize is [tex]\frac{20}{20000}[/tex]
A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each.
So, The value of prizes is
[tex]\frac{1}{20000}\times 1000+\frac{2}{20000}\times 300+\frac{20}{20000}\times 10[/tex]
If 20000 tickets are sold at 25 cents each i.e. $0.25.
Remaining tickets = 20000-1-2-20=19977
Probability of getting remaining tickets is [tex]\frac{19977}{20000}[/tex]
The expected value is
[tex]E=\frac{1}{20000}\times 1000+\frac{2}{20000}\times 300+\frac{20}{20000}\times 10-\frac{19977}{20000}\times 0.25[/tex]
[tex]E=\frac{1000+600+200-4994.25}{20000}[/tex]
[tex]E=\frac{-3194.25}{20000}[/tex]
[tex]E=-0.159[/tex]
Therefore, The expected winnings for a person buying 1 ticket is -0.2.
