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?

 Feb 5, 2020



I think I interpreted this one in the wrong way    !!!!!




cool cool cool

 Feb 5, 2020
edited by CPhill  Feb 5, 2020

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! )

 Feb 6, 2020

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



cool cool cool

CPhill  Feb 6, 2020

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.

Melody  Feb 8, 2020

What's the probability that the last cookie you eat is a butter cookie?  


p = 18/33 = 6/11 ≈ 0.545

 Feb 8, 2020

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