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# Probability

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Wu rolls two fair, six-sided dice.  You are not told what the rolls were, but you are told that the sum of the two rolls is a prime.  What is the probability that the sum of the two rolls is 2?

Oct 24, 2021

#2
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Wu rolls two fair, six-sided dice.  You are not told what the rolls were, but you are told that the sum of the two rolls is a prime.  What is the probability that the sum of the two rolls is 2?

Below is a table of all the possible combinations of two dice.

There is only 1 way to roll a 2, out of 36 possible rolls.

So the probability is 1/36.

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

.

Oct 24, 2021
#3
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There are:
(1,1), (1,2), (2,1), (1,4), (4,1), (1,6), (6,1), (2,3), (3,2), (2,5), (5,2), (3,4), (4,3), (5,6), (6,5)==15 ways of making up a prime on a roll of 2 dice.
And only 1 way of making up a 2 (1+1).

Therefore, the probability is: 1 / 15

Oct 25, 2021