This is a silly question, but I can't quite put my finger on where my reasoning is wrong.
Given a pair of 6 sided dice, what is the probability of rolling a 5 and a prime?
My answer: 6/36
Correct answer: 5/36
Probability of rolling a five = 1/6
Probability of rolling a prime = 3/6
Probability of first rolling a five and then a prime = 1/6*3/6 = 3/36
Probability of first rolling a prime and then a five = 3/6*1/6 = 3/36
Probability of rolling of rolling a five and a prime = 3/36+3/36 = 6/36
I think where my answer is wrong is that 5 is a prime itself and rolling (5,5) is double counted here.
Is there a better way of doing this type of problem to avoid making these mistakes in the future?
Thank you very much