Two dice are rolled, what is the probability that die 1 shows a 5 given that a 10 has been rolled?
I'm a little confused as to how to solve this exercise. I get two different results depending on how I go about solving it.
Method 1 (logic): The probability of having die 1 show a 5 when two dice are rolled is 1/36. The probability that a 10 is rolled is 3/36. Now I put this in the basic probability format and it gives me (1/36)/(3/36)=1/3.
Method 2 (baye's theorem): P(A/B) = P(A)xP(B/A) / P(B) = 1/36 x 1/6 (bc if die 1 shows a five and I need to get a 10, then die 2 needs to show a five also, hence 1/6) / (3/36) = 1/18