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%
