Question

What is the probability of rolling a number greater than or equal to 8 with the

sum of two dice, given that at least one of the dice must show a 6?

Answer 1

Answer: 5/18

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Step-by-step explanation:

I'll represent the dice results as an ordered pair. Something like (6,2) means the first die is a 6 and the second is a 2. The sum being 6+2 = 8.

There are only two ways to get to a sum of 8, and those two ways are:

• (6,2)
• (2,6)

Here are other possibilities if we allow the sum to be larger than 8

• (6,3)
• (6,4)
• (6,5)
• (6,6)
• (3,6)
• (4,6)
• (5,6)
• (6,6)

You should find that there are a total of 10 ways to have two dice add to a value that is 8 or larger, given that at least one of the dice must be a 6.

This is out of 6*6 = 36 ways to roll two dice without such a restriction. The probability we're after is 10/36 = (2*5)/(2*18) = 5/18

Side note: 5/18 = 0.2778 = 27.78% approximately