Question

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?

Answer 1

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

Step-by-step 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