Question

Skyler buys a bag of cookies that contains 9 chocolate chip cookies, 5 peanut butter cookies, 9 sugar cookies and 7 oatmeal raisin cookies. What is the probability that Skyler randomly selects an oatmeal raisin cookie from the bag, eats it, then randomly selects another oatmeal raisin cookie?

Answer 1

Answer:   $\dfrac{7}{145}$ .

Step-by-step explanation:

Given ,The bag contains :

9 chocolate chip cookies, 5 peanut butter cookies, 9 sugar cookies and 7 oatmeal raisin cookies.

Total cookies = 9+5+9+7=30

Now , the number of ways to choose any two cookies ( one after another) :

$^{30}C_2=\dfrac{30!}{2!(30-2)!}=\dfrac{30\times29\times28!}{2\times28!}=435$

The number of way to choose two oatmeal raisins ( one after another) :

$^{7}C_2=\dfrac{7!}{2!(7-2)!}=\dfrac{7\times6\times5!}{2\times5!}=21$

Now , the probability that Skyler randomly selects an oatmeal raisin cookie from the bag, eats it, then randomly selects another oatmeal raisin cookie will be :

$\dfrac{21}{435}=\dfrac{7}{145}$

Hence, the required probability is $\dfrac{7}{145}$ .