Question

Two dice are rolled. Determine the probability of the following: rolling a 6 or doubles

Answer 1

Answer as an exact fraction = 5/18

Answer as an approximate decimal = 0.2778

Answer as an approximate percentage = 27.78%

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Explanation:

x = result of the first die

y = result of the second die

(x,y) paired together shows the results of both dice at the same time.

Something like (x,y) = (4,2) means we got 4 on the first die and 2 on the second die.

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Let's list the ways of rolling a 6

• (1,5)
• (2,4)
• (3,3)
• (4,2)
• (5,1)

There are 5 ways to roll a 6. Each pair listed has the property x+y = 6.

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List all the ways of getting doubles

• (1,1)
• (2,2)
• (3,3)
• (4,4)
• (5,5)
• (6,6)

There are 6 ways to roll doubles. Each pair mentioned has x = y.

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We have 5+6 = 11 items listed above. However, there are only 10 unique pairs though because (3,3) was listed twice. So we could say 5+6-1 = 11-1 = 10.

This is out of 6*6 = 36 different ways to roll the two dice. The probability is therefore 10/36 = 5/18.

Using a calculator, 5/18 = 0.2778 = 27.78%