The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 600 tickets. There is one $3,000 grand prize, four $400 second prizes, and eighteen $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

Question
Asked Oct 25, 2019

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 600 tickets. There is one $3,000 grand prize, four $400 second prizes, and eighteen $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

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Expert Answer

Step 1

It is given that the number of tickets is 600 and the numbers of prizes are 1 grand, 4 second, and 18 third, respectively.

First prize’s value is 3000$, second prize’s value is 400$, and third prize’s value is 30$

Consider that X1, X2, and X3 are the random variables defined as the grand prize, second prize, and third prize respectively.

Probability of selecting grand prize is:

Number of grand prizes
P(X)
Total number of tickets
1
600
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Number of grand prizes P(X) Total number of tickets 1 600

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Step 2

Similarly,

Probability of select...

4
P(X,)
600
Probability of selecting third prize is:
18
P(X;)=
600
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4 P(X,) 600 Probability of selecting third prize is: 18 P(X;)= 600

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