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A company offers a raffle whose grand prize is a $35,000 new car. Additional prizes are a $1,100 television and $600 computer. Tickets cost $22 each, Ticket incme over the cost the prizes will be donated to charity. If 3,000 tickets are sold, what is the expected gain loss (in dollars) of each ticket? (Round your answer to the nearest cent.) Need Help? Talk to a Tutor Read It

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Answer:

-$ 10.13

Step-by-step explanation:

Given,

The cost price of each ticket = $ 22,

So, the value of each ticket other than price ticket = - $ 22, ( negative sign shows loss,i.e. if we don't get the price we will have the loss of $ 22 )

Now, there are 3 tickets in which first is of $35,000 price, second is of $1,100 and third is of $ 600,

So, the value of first ticket = 35000 - 22 = $ 34978,

Value of second ticket = 1100 - 22 = $ 1078,

Value of third ticket = 600 - 22 = $ 578,

Also,

[tex]\text{Probability}=\frac{\text{Favourable outcome}}{\text{Total outcome}}[/tex]

Hence, by the above information we can make a table for the given situation,

Number           2997               1                    1                     1        

Price               -$ 22               $ 34978        $ 1078           $ 578

Probability       2997/3000      1/3000         1/3000           1/3000

Therefore, the expected value of a ticket

[tex]=-22\times \frac{2997}{3000}+34978\times \frac{1}{3000}+578\times \frac{1}{3000}[/tex]

[tex]=-$10.126[/tex]

≈ - $ 10.13

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