Question

A large cookie jar contains the following selection of mini-cookies: 10 sugar, 14 oatmeal raisin, 18 peanut butter, and 6 chocolate chip cookies. You randomly select 2 cookies, one at a time, without replacement.

Compute the following probabilities.

(a) probability of getting 2 peanut butter cookies 0.375

(b) probability of getting 2 sugar cookies 0.208

(c) probability of not getting 2 sugar cookies

(d) probability of getting one oatmeal raisin and then one chocolate chip cookie

Show all calculator commands and round your answer to 3 decimal places.

Answer 1

P(A) = n(E)/n(S)

Where P(A) is the probability of an event A

n(E) is the number of favorable outcomes

n(S) is the total number of events in the sample space.      

10 sugar, 14 oatmeal raisin, 18 peanut butter, and 6 chocolate chip cookies. A total of 48

a)

P = P(selecting first a peanut butter cooky) * P(selecting second a peanut butter cooky)

P = (18 / 48) * (17 / 47) = 306 / 2256 = 0.136

b)

P = P(selecting first a sugar cooky) * P(selecting second a sugar cooky)

P = (10 / 48) * (9 / 47) = 90 / 2256 = 0.040

c)

Not getting 2 sugar cooky = 1 - getting sugar cooky = 1 - 0.04 = 0.960

d)

P = P(selecting first a oatmeal cooky) * P(selecting second a chocolate chip cooky)

P = (14 / 48) * (6 / 47) = 84 / 2256 = 0.037