QR- Destroyer - Probability Question

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belmont3

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In craps, you roll 2 dice. You can win on the first roll if you roll a 7 or an 11, and you lose if you roll a 2, 3, or 12. Any other number becomes a point and the game continues. What is the probability of winning or losing on the first roll?

a) 1
b) 5/12
c) 1/2
d) 1/3
e) 1/4

Please provide full explanation with the solution. Thank you!

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StumpMT

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In order to win you need to roll a 7 or 11. There are 8 ways this can occur (1,6) (6,1) (2,5) (5,2) (3,4) (4,3) (5,6) or (6,5).
In order to lose you need to roll a 2, 3, or 12. There are 4 ways this can occur (1,1) (1,2) (2,1) or (6,6).
The probability of rolling one dice combination is 1/36 (1/6 on one dice and 1/6 on the other dice).

The problem is asking what the probability is for winning OR losing. So now that we know how many different combinations there are in order to win or lose, and we know the probability of one combination all we do is add up the probabilities for each combination ie 1/36 + 1/36 + 1/36, etc. This will give us 12/36 or 1/3. There is a 1/3 chance you will win or lose on the first roll.
 
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