I recently asked this question:
Roll a fair 6 sided die twice, What is the probability that one or both rolls are 6?
And that makes sense, however, the reason I was confused in the first place is because we went over the following question during section:
Suppose the six-sided die you used in the previous problem is not fair. It is biased
so that rolling a 6 is three times more likely than any other roll.
This leads to the chance of a 6 being 3/8 and the chance of 1-5 being 1/8.
What is the probability that one or both rolls are 6’s?
However, my TA told me that there would be no overlap, and therefore nothing to subtract. However, my question that I asked previously, involving an unbiased die did involve overlap.
Was my TA wrong, is there overlap in this question? Or more specifically, is the answer 3/8 (prob of first roll being 6) + 3/8 (prob of second roll being 6) – 9/64 (prob of both being 6)
Thanks a bunch.
Best Answer
As lulu mentioned overlap certainly matters. In fact you can prove it does using the following principle. https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle