If 2 fair dice are rolled, what is the probability that the sum is 6, given both dice show odd numbers?
When the sum is 6, there combinations are: (1,5),(2,4),(3,3),(4,2),(5,1). Probability = 5/36
Probability of 2 odd numbers is 1/2.
What I'm not sure about is when we work out Pr(sum is 6|both numbers odd). I initially thought that the top line was Pr(sum is 6), but then the result would be 5/2. This can't be right.
So, does that mean that we only choose combinations which have odd pairs? So, the answer would be 3/2?
Still makes no sense as the number is greater than 1???
Can somebody shed some light on this for me?
Best Answer
What you're trying to compute is the probability that two dice sum to $6$, given that both dice have odd values. Note that there are three ways for pairs of dice with odd values to sum to six, namely $(1,5),(3,3),(5,1)$. There are three odd values each die can take, so there are nine ways for pairs of dice to both have odd values. Thus the probability you are looking for is $3/9=1/3$.