Question
Asked Dec 11, 2019
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A pair of fair 6-sided dice is rolled. What is the probability that a 2 is rolled if it is known that the sum of the numbers landing uppermost is less than or equal to 6? (Enter your answer as an exact fraction.)

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Expert Answer

Step 1

When we rolled two dice then the possible outcome or sample space is,

{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

Step 2

Total number of possible outcome that the sum of the numbers landing uppermost is less than or equal to 6 = 15

Total number of possible outcome that contains number 2 where the sum of the numbers landing uppermost is less than or equal to 6 = 7

Step 3

Now, the probability (P) that a 2 is rolled if it is known that the sum of the n...

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Favorable outcome P = Total outcome 15

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