Six-sided Die

A 6-sided die is labeled with the first prime numbers instead of the first integers 1 to 6. The die is rolled twice. What is the probability that the sum of the rolls is a prime number?
Source: NCTM Mathematics Teacher 2008

SOLUTION
Table method

The table shows there are 6 outcomes in which the sum of the rolls is a prime number.
Probability = 6/36=1/6.

Alternative method
Number of possible outcomes
6\times 6=36
Number of desirable outcomes
We need only look at the sum of 2+x because we want an odd sum
2+3=5
2+5=7
2+7=9
2+11=13
2+13=15
Of these sums only 5,7, and 13 are prime number. We double the count to 6 because we could toss 2 and 3 or 3 and 2.
Probability = 6/36=1/6.

Answer: 1/6

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About mvtrinh

Retired high school math teacher.
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