Find the expected value for your profit

Question

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $8 each and will sell 600 tickets. There is one $1,000 grand prize, three $500 second prizes, and thirteen $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

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Answer 1

Hi Anni,

First, compute the profit for each scenario.

Grand Prize Winner: 1000-8 = 992

Second Prize Winner: 500-8 = 492

Third Prize Winner: 30-8 = 22

Nothing: 0-8 = -8

Now, let's look at probabilities. Most textbooks will do this as a table, but that's tough in Wyzant's platform

P(Grand) = 1/1000

P(Second)= 3/1000

P(Third)= 30/1000

P(Loss) = (1000 - 34)/1000

P(Loss) = 966/1000

Now, multiply each probability by the amount of profit associated with the outcome and sum for the expected value:

E(x) = [(1/1000)(992)] + [(3/1000)(492)] + [(30/1000)(22)] + [(966/1000)(-8)]

E(x) = 0.992 + 1.476 + 0.66 + -7.728

E(x) = -4.6

You can expect to lose about $4.60 on average by buying this ticket. I hope this helps.