06/19/2020 (2011: Countdown Round, Problem 6)

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Q: Filipe rolls two standard, six-sided dice. What is the probability that he rolls a sum that is a prime number? Express your answer as a common fraction.

A: 5/12
We can make a table where we show each of the possibilities. The topmost row and leftmost column are the numbers on the dice and the other numbers are the possible combinations. The highlighted numbers are the prime possibilities:
 
12
3
4
5
6
1
2
3
4
5
6
7
23
4
5
6
7
8
34
5
6
7
8
9
45
6
7
8
9
10
56
7
8
9
10
11
678
9
10
11
12
There are 15 prime (highlighted) numbers out of the 36 total choices. 15/36 = 5/12.

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