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If a 6, 7, or 8 shows up on a roll of a pair of dice, you win two dollars.  If anything else shows up, you lose one dollar.  If you roll the dice 300 times, what is your expected amount of winnings?

 Jun 2, 2020
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Of the 36 possible combinations of the rolling of two dice

  a 6 can appear 5 ways

  a 7 can appear 6 ways

an 8 can appear 5 ways.

 

So, there is a total of 5 + 6 + 5  =  16 ways to win out of the 36 possibilities.

Probability of winning:  16/36.

 

This means that there are 36 - 16  =  20 ways to lose.

Probability of losing:  20/36

 

Expected winnings:  300 x [ 16/36 x $2.00 - 20/36 x $1.00 ]  =  .....

 Jun 2, 2020

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