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At a festival you run across a booth with an interesting game. Tokens are sold for $2 with a selection of prizes. There is a $25 grand prize which you have a 5% chance of winning, there are 5 mid-level prizes, each worth $15 with a 15% chance of winning, and there is a consolation prize worth $1 with a 20% chance of winning. What is your expected gain or loss if you play this game

Respuesta :

Answer:

Your expected gain is of $10.7.

Step-by-step explanation:

Expected earnings:

The expected earnings is each prize multiplied by it's probability of being earned.

So

5% probability of earning $25.

5*15% = 75% probability of earning $15.

20% probability of earning $1. So

0.05*25 + 0.75*15 + 0.2*1 = 12.7

Cost of token:

The token costs $2, which means that we subtract $2 from the expected earnings.

12.7 - 2 = 10.7

Your expected gain is of $10.7.

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