John rolls a pair of standard 6-sided dice. What is the probability that the two numbers he rolls are relatively prime? Express your answer as a common

EP: The question is NOT about primes! The two numbers, it says, are "relatively prime"!.

Relatively Prime: Describes two numbers for which the only common factor is 1. In other words, relatively prime numbers have a greatest common factor (gcf) of 1. For example, 6 and 35 are relatively prime (gcf = 1).

We have to use a little bit of casework to solve this problem. If the first die shows a 1, the second die can be anything (6 cases). If the first die shows 2 or 4, the second die is limited to 1, 3, or 5 (2 * 3 = 6 cases). If the first die shows 3, the second die can be 1, 2, 4, or 5 (4 cases). If the first die shows 5, the second die can be anything but 5 (5 cases). If the first die shows 6, the second die can be only 1 or 5 (2 cases). There are 36 ways to roll two dice, 23 of which are valid, so the answer is 23/36.

Well there are 36 possible rolls

there are three  possible primes on each die    2, 3 and  5

you can roll a

2 & 2

2 & 3

2 & 5

3 & 2

3 & 3

3 & 5

5 & 2

5 & 3

5 & 5

Those are the only 9 rolls that have TWO primes      9 out of 36 rolls     9/36   or   1 /4   

John rolls a pair of standard 6-sided dice. What is the probability that the two numbers he rolls are relatively prime? Express your answer as a common fraction.

Great work Ninja :)

sorry EP our guest is right :(

Thanks for the explanation guest. :)

\(P(relatively \;prime)=\frac{23}{36}\)