# I offer you a game where I give you \$30.00 if you roll a "1" or a "2" on a standard fair dice. otherwise, if you roll anything else, you pay \$12.a. is this fair game?b. what is the expected value?c> hojw much would you expect to make or lose in 100 rolls?

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I offer you a game where I give you \$30.00 if you roll a "1" or a "2" on a standard fair dice. otherwise, if you roll anything else, you pay \$12.
a. is this fair game?
b. what is the expected value?
c> hojw much would you expect to make or lose in 100 rolls?

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Step 1

We start by finding the probability of the various situations. Since there are 6 faces of a dice and it is a fair dice the probability of rolling any face is 1/6. Hence the total probability of rolling “1” or “2” is 1/6 + 1/6 = 2/6 and the probability of rolling anything else is 1 – 2 /6 = 4/6 (using rule of complements in probability theory).

Hence the expected value of rolling a dice is the weighted average of the payments (positive of negative) weight...

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