Question

You roll two dice as part of a casino game. Express your answers as reduced fractions.Find the probability of rolling a sum of 6, 7, or 8.

Answer 1

Answer: 7/12

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Step-by-step explanation:

Let's list the ways to roll a 6.

• 1+5 = 6
• 2+4 = 6
• 3+3 = 6
• 4+2 = 6
• 5+1 = 6

There are A = 5 items listed above.

Now let's list the ways to roll a sum of 7.

• 1+6 = 7
• 2+5 = 7
• 3+4 = 7
• 4+3 = 7
• 5+2 = 7
• 6+1 = 7

There are B = 6 items listed above.

Lastly, let's list the ways to roll a sum of 8.

• 2+6 = 8
• 3+5 = 8
• 4+4 = 8
• 5+3 = 8
• 6+2 = 8

There are C = 5 items listed above.

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Summary so far:

We found there are

• A = 5 ways to roll a "6"
• B = 6 ways to roll a "7"
• C = 5 ways to roll an "8"

Therefore, we have A+B+C = 6+7+8 = 21 ways to roll either of those three sums. Each event is mutually exclusive.

This is out of 6*6 = 36 ways to roll two dice (whether we get those sums or not).

21/36 = (7*3)/(12*3) = 7/12 is the probability of getting any of those three sums mentioned.

7/12 = 0.5833 = 58.33% approximately