I made three batches of 15 cookies each and combined them all into one big cookie jar. My first batch consisted of a 9 chocolate chip cookies, 4 snickerdoodles, and 2 oatmeal raisin cookies. My second batch consisted of 3 chocolate chip cookies, 8 snickerdoodles, and 4 oatmeal raisin cookies. My third batch consisted of 7 chocolate chip cookies, 3 snickerdoodles, and 5 oatmeal raisin cookies. Consider the following 3 scenarios (each scenario is unrelated to the others)

a. I want three cookies and take them out of the jar. What is the probability that all three are chocolate chip cookies?
b. I pick a cookie from the jar and it’s a chocolate chip cookie. What is the probability that I baked it in my first batch?
c. I hate snickerdoodles, don’t want them, and don’t think they deserve to exist. I will take cookies from the jar one at a time. If I get a snickerdoodle, I will throw it in the trash and pick another cookie. If I get a chocolate chip or oatmeal raisin cookie, I will put it aside to eat and continue until I have put aside 3 cookies to eat. What is the expected number of snickerdoodles that will be left in the jar when I’m done?

a. The probability that all three cookies taken out of the jar are chocolate chip cookies = 42%

b.  The probability that a cookie picked from the jar, which is a chocolate chip cookie, is baked in the first batch = 27%

c. c. The expected number of snickerdoodles that will be left in the jar after is:

11

Explanation:

a) Data and Calculations:

Batches  Chocolate   Snickerdoodles  Oatmeal Raisin    Total

First                9                      4                       2                    15

Second          3                       8                       4                    15

Third              7                       3                       5                    15

Total            19                      15                      11                    45

a. Probability that all three cookies taken out of the jar are chocolate chip cookies = 19/45 = 0.42222 = 42%

b. The probability that a cookie picked from the jar, which is a chocolate chip cookie, is baked in the first batch = 4/15 = 0.26666 = 27%

c. The expected number of snickerdoodles that will be left in the jar after setting 3 cookies aside is:

Probability of picking snickerdoodles

3/45 * 1/11 = 11/45 = 0.02222

Remaining snickerdoodles = (1 - 0.02222) * 11 = 10.75 = 11