Question

Suppose your friend has 10 cookies 3 of which are chocolate chip. Your friend randomly divides the cookies equally between herself and you. What is the probability that you get all the chocolate chip cookies?​

Answer 1

Answer:

3/10

0.3 probability that you get all the chocolate cookiee

Answer 2

Given:

your friend has 10 cookies 3 of which are chocolate chip

Let random variable  X=  number of chocolate chip cookies you get.

Then  X  is hypergeometric with  N=10  total cookie

m=3  chocolate chip cookies

and  n=5  cookies selected by your friend to give to you.

We want the probability that you get all the chocolate chip cookies, i.e.,  P(X=3) , which is

$P(X=3)=\frac{\left(\begin{array}{l}3 \\3\end{array}\right)\left(\begin{array}{l}7 \\2\end{array}\right)}{\left(\begin{array}{c}10 \\5\end{array}\right)}$

P(X=3) = 0.083