QuestionBrigeth has 5 chocolate chip, 5 peanut butter, 4 sugar, and 9 oatmeal cookies. Find the probability of selecting 2 chocolate chip cookies.

Studdy Solution

STEP 1

Assumptions1. The bag contains5 chocolate chip cookies,5 peanut butter cookies,4 sugar cookies and9 oatmeal raisin cookies. . Brigeth randomly selects a cookie from the bag each time.
3. After selecting a cookie, Brigeth eats it, meaning it is removed from the bag.

STEP 2

First, we need to find the total number of cookies in the bag. We can do this by adding the number of each type of cookie.
$Total\, cookies = Chocolate\, chip\, cookies + Peanut\, butter\, cookies + Sugar\, cookies + Oatmeal\, raisin\, cookies$

STEP 3

Now, plug in the given values for the number of each type of cookie to calculate the total number of cookies.
$Total\, cookies =5 +5 + +9$

STEP 4

Calculate the total number of cookies in the bag.
$Total\, cookies = + +4 +9 =23$

STEP 5

The probability of selecting a chocolate chip cookie on the first draw is the number of chocolate chip cookies divided by the total number of cookies.
$(Chocolate\, chip\,1st) = \frac{Chocolate\, chip\, cookies}{Total\, cookies}$

STEP 6

Plug in the values for the number of chocolate chip cookies and the total number of cookies to calculate the probability of selecting a chocolate chip cookie on the first draw.
$(Chocolate\, chip\,1st) = \frac{5}{23}$

STEP 7

After eating the first chocolate chip cookie, there are now4 chocolate chip cookies left and22 total cookies. The probability of selecting another chocolate chip cookie is the number of chocolate chip cookies divided by the total number of cookies.
$(Chocolate\, chip\,2nd) = \frac{Chocolate\, chip\, cookies -1}{Total\, cookies -1}$

STEP 8

Plug in the values for the number of chocolate chip cookies and the total number of cookies to calculate the probability of selecting another chocolate chip cookie.
$(Chocolate\, chip\,2nd) = \frac{4}{22}$

STEP 9

The probability of both events happening (selecting a chocolate chip cookie, eating it, then selecting another chocolate chip cookie) is the product of the individual probabilities.
$(Both) =(Chocolate\, chip\,st) \\times(Chocolate\, chip\,2nd)$

STEP 10

Plug in the values for the probability of selecting a chocolate chip cookie on the first draw and the probability of selecting another chocolate chip cookie to calculate the probability of both events happening.
$(Both) = \frac{5}{23} \\times \frac{4}{22}$

STEP 11

Calculate the probability of both events happening.
$(Both) = \frac{5}{23} \\times \frac{4}{22} = \frac{20}{506} = \frac{10}{253} \approx0.040$ The probability that Brigeth randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects another chocolate chip cookie is $\frac{10}{253}$ or approximately0.040.

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