Skyler buys a bag of cookies that contains 4 chocolate chip cookies, 6 peanut butter cookies, 9 sugar cookies and 6 oatmeal raisin cookies. What is the probability that Skyler randomly selects a sugar cookie from the bag, eats it, then randomly selects another sugar cookie? Express your answer as a reduced fraction.

 

The probability is 3/25

Check below for explanation.

Step-by-step explanation

There are Initially 4 chocolate chip cookies, 6 peanut butter cookies, 9 sugar cookies and 6 oatmeal raisin cookies.

So, total number of cookies= 4+6+9+6= 25

Number of sugar cakes=9

So, probability of getting a sugar cookie on first pick= Number of sugar cakes/total number of cookies

= 9/25

Now. if she takes a sugar cookie on first time, then there is one less sugar cookie in the bag. So now,

total number of cookies= 24

Number of sugar cakes=8

So, probability of getting a sugar cookie on second pick= Number of sugar cakes/total number of cookies

= 8/24

Since these are two independent events, combined probability will be the product of two individual probabilities.

So,

Total probability= 8/24*9/25 = 1/3*9/25 = 3/25

Feel free to ask if you require any further clarifications.