Question

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?

Answer 1

Answer:

9.64 *10^-10

Step-by-step explanation:

The jar contains 15 chocolate chip and 18 butter cookies

probability that the first cookie you ate is chocolate chip cookie = 15/33.

Now, there are remaining 14 chocolate chip cookies and 32 total cookies i the jar.

probability that the second cookie you ate is also chocolate chip cookie =  14/32.

probability that you ate all the chocolate chip cookies first =  $\frac{15!}{33!/18!}$

probability that you ate all the butter cookies  after = $\frac{18!}{18!}$ = 1

probability that you ate all the chocolate chip cookies before you ate all the butter cookies = $\frac{15!}{33!/18!} * 1 = \frac{15! * 18!}{33!} = \frac{15! * 18!}{33!}$

= 9.64 *10^-10