contestada

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?

Respuesta :

anthougo

Answer:

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

Otras preguntas