Question

Catherine buys a bag of cookies that contains 8 chocolate chip cookies, 9 peanut butter cookies, 5 sugar cookies and 7 oatmeal cookies. What is the probability that Catherine randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie? Express you answer as a reduced fraction.

Answer 1

The probability of Catherine first selecting a sugar cookie and then an oatmeal cookie from a bag containing different types of cookies is 5/116, determined by multiplying the individual probabilities of each selection.

Step-by-step explanation:

To solve this problem, we need to determine the probability of two dependent events occurring in sequence. Firstly, Catherine buys a bag containing 8 chocolate chip cookies, 9 peanut butter cookies, 5 sugar cookies, and 7 oatmeal cookies, making a total of 29 cookies. The probability of Catherine selecting a sugar cookie first is thus 5 out of 29 (5/29). After eating the sugar cookie, there are 28 cookies left in the bag, including 7 oatmeal cookies. The probability that she then selects an oatmeal cookie is 7/28, or 1/4 when reduced.

To find the overall probability of both events occurring, we multiply the probabilities of each event:

Probability of selecting a sugar cookie and then an oatmeal cookie = (5/29) * (1/4)

= 5/116 when the fraction is simplified. This is the probability of the two-step event occurring.

Answer 2

Step-by-step explanation:

Given: 8 chocolate chip cookies, 9 peanut butter cookies, 5 sugar cookies and 7 oatmeal cookies.

=> Total cookies are: 29

• The possible outcomes of sugar cookie:
  `C^(1) _(5)` = 5 and the total possible outcomes: 25

• The possible outcomes of oatmeal cookie:
  `C^(1) _(7)` = 7 the total possible outcomes 25-1 =24 because Catherine eats it

The probability that Catherine randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie:

P(sugar then oatmeal) =
`(5)/(25) (7)/(24)` =
`(7)/(120)` = 0.058