Question

A jar contains 3 peanut butter cookies, 6 caramel delights, and 9 lemon cookies. If 3 cookies are selected in succession, find the probability of selecting one of each if no cookies are replaced.

Options:
A) 0.15
B) 0.20
C) 0.25
D) 0.30

Answer 1

The probability of selecting one of each cookie is 0.03.

Step-by-step explanation:

To find the probability of selecting one of each cookie, we need to calculate the probability of selecting a peanut butter cookie, a caramel delight, and a lemon cookie in succession without replacement.

The total number of cookies in the jar is 3 + 6 + 9 = 18.

The probability of selecting a peanut butter cookie is 3/18.

After selecting a peanut butter cookie, there are 17 cookies left in the jar, including 6 caramel delights. So, the probability of selecting a caramel delight is 6/17.

After selecting a caramel delight, there are 16 cookies left, including 9 lemon cookies. Therefore, the probability of selecting a lemon cookie is 9/16.

The probability of selecting one of each cookie is (3/18) * (6/17) * (9/16) = 0.031.

Rounded to two decimal places, the probability is approximately 0.03.