A jar contains 15 chocolate chip and 18 butter cookies.a) If you eat them randomly one at a time (so you are equally likely to choose any cookie in the jarwhen you eat one), what is the probability that you eat all the chocolate chip cookies before you eat allthe butter cookies?
You start with 15 cc cookies and 33 total cookies.
The probability that the first cookie is cc is 15/33.
Now, there are 14 cc cookies and 32 total cookies.
The probability that the second cookie is cc is 14/32.
Continue this pattern and multiply all the individual probabilities together:
(15/33) x (14/32) x (13/31) x (12/30) x ... x (2/20) x (1/19) = your answer
or: 15! / ( 33! / 18! )
That was my original answer, too, Geno
But...as EP pointed out to me, we both interpreted this as eating all the chocolate chips BEFORE eating ANY of the butter cookies....however......the question seems to be implying that we want the probability of eating all the chocolate chips BEFORE eating ALL the butter cookies.......this answer is probably somewhat different
You raise an interesting point Chris.
I do not think you have enough information to answer the question as you interpret it. (And I think your interpretation is the literal one)
You would need probabilities related to eating another cookie if you had already eaten x number of cookies. and you are not given that.