QuestionWhat is the probability that Jonah picks an oatmeal cookie and then a sugar cookie from a bag of 6 chocolate chip, 5 peanut butter, 5 sugar, and 7 oatmeal cookies? Express as a reduced fraction.

Studdy Solution

STEP 1

Assumptions1. The bag contains6 chocolate chip cookies,5 peanut butter cookies,5 sugar cookies and7 oatmeal cookies. . Jonah randomly selects a cookie from the bag each time.
3. After selecting a cookie, Jonah eats it, meaning it is removed from the bag and cannot be selected again.

STEP 2

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

STEP 3

Now, plug in the given values for the number of each type of cookie to calculate the total number of cookies.
$Total\, cookies =6 +5 +5 +7$

STEP 4

Calculate the total number of cookies in the bag.
$Total\, cookies =6 + + +7 =23$

STEP 5

The probability of randomly selecting an oatmeal cookie from the bag is the number of oatmeal cookies divided by the total number of cookies.
$(Oatmeal) = \frac{atmeal\, cookies}{Total\, cookies}$

STEP 6

Plug in the values for the number of oatmeal cookies and the total number of cookies to calculate the probability of selecting an oatmeal cookie.
$(Oatmeal) = \frac{}{23}$

STEP 7

After Jonah eats the oatmeal cookie, the total number of cookies in the bag decreases by one. So, the new total number of cookies is $New\, total\, cookies = Total\, cookies -1$

STEP 8

Calculate the new total number of cookies in the bag.
$New\, total\, cookies =23 -1 =22$

STEP 9

The probability of randomly selecting a sugar cookie from the bag after eating the oatmeal cookie is the number of sugar cookies divided by the new total number of cookies.
$(Sugar) = \frac{Sugar\, cookies}{New\, total\, cookies}$

STEP 10

Plug in the values for the number of sugar cookies and the new total number of cookies to calculate the probability of selecting a sugar cookie.
$(Sugar) = \frac{5}{22}$

STEP 11

The probability of both events happening (selecting an oatmeal cookie and then a sugar cookie) is the product of the individual probabilities.
$(Oatmeal\, and\, Sugar) =(Oatmeal) \\times(Sugar)$

STEP 12

Plug in the values for the probability of selecting an oatmeal cookie and the probability of selecting a sugar cookie to calculate the probability of both events happening.
$(Oatmeal\, and\, Sugar) = \frac{7}{23} \\times \frac{5}{22}$

STEP 13

Calculate the probability of both events happening.
$(Oatmeal\, and\, Sugar) = \frac{7}{23} \\times \frac{5}{22} = \frac{35}{506}$ The probability that Jonah randomly selects an oatmeal cookie from the bag, eats it, then randomly selects a sugar cookie is35/506.

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QuestionWhat is the probability that Jonah picks an oatmeal cookie and then a sugar cookie from a bag of 6 chocolate chip, 5 peanut butter, 5 sugar, and 7 oatmeal cookies? Express as a reduced fraction.

Studdy Solution

STEP 1

Assumptions1. The bag contains6 chocolate chip cookies,5 peanut butter cookies,5 sugar cookies and7 oatmeal cookies. . Jonah randomly selects a cookie from the bag each time.
3. After selecting a cookie, Jonah eats it, meaning it is removed from the bag and cannot be selected again.

STEP 2

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

STEP 3

Now, plug in the given values for the number of each type of cookie to calculate the total number of cookies.
$Total\, cookies =6 +5 +5 +7$

STEP 4

Calculate the total number of cookies in the bag.
$Total\, cookies =6 + + +7 =23$

STEP 5

The probability of randomly selecting an oatmeal cookie from the bag is the number of oatmeal cookies divided by the total number of cookies.
$(Oatmeal) = \frac{atmeal\, cookies}{Total\, cookies}$

STEP 6

Plug in the values for the number of oatmeal cookies and the total number of cookies to calculate the probability of selecting an oatmeal cookie.
$(Oatmeal) = \frac{}{23}$

STEP 7

After Jonah eats the oatmeal cookie, the total number of cookies in the bag decreases by one. So, the new total number of cookies is $New\, total\, cookies = Total\, cookies -1$

STEP 8

Calculate the new total number of cookies in the bag.
$New\, total\, cookies =23 -1 =22$

STEP 9

The probability of randomly selecting a sugar cookie from the bag after eating the oatmeal cookie is the number of sugar cookies divided by the new total number of cookies.
$(Sugar) = \frac{Sugar\, cookies}{New\, total\, cookies}$

STEP 10

Plug in the values for the number of sugar cookies and the new total number of cookies to calculate the probability of selecting a sugar cookie.
$(Sugar) = \frac{5}{22}$

STEP 11

The probability of both events happening (selecting an oatmeal cookie and then a sugar cookie) is the product of the individual probabilities.
$(Oatmeal\, and\, Sugar) =(Oatmeal) \\times(Sugar)$

STEP 12

Plug in the values for the probability of selecting an oatmeal cookie and the probability of selecting a sugar cookie to calculate the probability of both events happening.
$(Oatmeal\, and\, Sugar) = \frac{7}{23} \\times \frac{5}{22}$

STEP 13

Calculate the probability of both events happening.
$(Oatmeal\, and\, Sugar) = \frac{7}{23} \\times \frac{5}{22} = \frac{35}{506}$ The probability that Jonah randomly selects an oatmeal cookie from the bag, eats it, then randomly selects a sugar cookie is35/506.

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QuestionWhat is the probability that Jonah picks an oatmeal cookie and then a sugar cookie from a bag of 6 chocolate chip, 5 peanut butter, 5 sugar, and 7 oatmeal cookies? Express as a reduced fraction.

Studdy Solution

STEP 1

Assumptions1. The bag contains6 chocolate chip cookies,5 peanut butter cookies,5 sugar cookies and7 oatmeal cookies. . Jonah randomly selects a cookie from the bag each time.3. After selecting a cookie, Jonah eats it, meaning it is removed from the bag and cannot be selected again.

STEP 2

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=6+5+5+7Total\, cookies =6 +5 +5 +7Totalcookies=6+5+5+7

STEP 4

Calculate the total number of cookies in the bag.Total cookies=6+++7=23Total\, cookies =6 + + +7 =23Totalcookies=6+++7=23

STEP 5

The probability of randomly selecting an oatmeal cookie from the bag is the number of oatmeal cookies divided by the total number of cookies.(Oatmeal)=atmeal cookiesTotal cookies(Oatmeal) = \frac{atmeal\, cookies}{Total\, cookies}(Oatmeal)=Totalcookiesatmealcookies​

STEP 6

Plug in the values for the number of oatmeal cookies and the total number of cookies to calculate the probability of selecting an oatmeal cookie.(Oatmeal)=23(Oatmeal) = \frac{}{23}(Oatmeal)=23​

STEP 7

After Jonah eats the oatmeal cookie, the total number of cookies in the bag decreases by one. So, the new total number of cookies isNew total cookies=Total cookies−1New\, total\, cookies = Total\, cookies -1Newtotalcookies=Totalcookies−1

STEP 8

Calculate the new total number of cookies in the bag.New total cookies=23−1=22New\, total\, cookies =23 -1 =22Newtotalcookies=23−1=22

STEP 9

STEP 10

Plug in the values for the number of sugar cookies and the new total number of cookies to calculate the probability of selecting a sugar cookie.(Sugar)=522(Sugar) = \frac{5}{22}(Sugar)=225​

STEP 11

The probability of both events happening (selecting an oatmeal cookie and then a sugar cookie) is the product of the individual probabilities.(Oatmeal and Sugar)=(Oatmeal)times(Sugar)(Oatmeal\, and\, Sugar) =(Oatmeal) \\times(Sugar)(OatmealandSugar)=(Oatmeal)times(Sugar)

STEP 12

Plug in the values for the probability of selecting an oatmeal cookie and the probability of selecting a sugar cookie to calculate the probability of both events happening.(Oatmeal and Sugar)=723times522(Oatmeal\, and\, Sugar) = \frac{7}{23} \\times \frac{5}{22}(OatmealandSugar)=237​times225​

STEP 13

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Assumptions1. The bag contains6 chocolate chip cookies,5 peanut butter cookies,5 sugar cookies and7 oatmeal cookies. . Jonah randomly selects a cookie from the bag each time.
3. After selecting a cookie, Jonah eats it, meaning it is removed from the bag and cannot be selected again.

Now, plug in the given values for the number of each type of cookie to calculate the total number of cookies.
$Total\, cookies =6 +5 +5 +7$

Calculate the total number of cookies in the bag.
$Total\, cookies =6 + + +7 =23$

The probability of randomly selecting an oatmeal cookie from the bag is the number of oatmeal cookies divided by the total number of cookies.
$(Oatmeal) = \frac{atmeal\, cookies}{Total\, cookies}$

Plug in the values for the number of oatmeal cookies and the total number of cookies to calculate the probability of selecting an oatmeal cookie.
$(Oatmeal) = \frac{}{23}$

After Jonah eats the oatmeal cookie, the total number of cookies in the bag decreases by one. So, the new total number of cookies is $New\, total\, cookies = Total\, cookies -1$

Calculate the new total number of cookies in the bag.
$New\, total\, cookies =23 -1 =22$

Plug in the values for the number of sugar cookies and the new total number of cookies to calculate the probability of selecting a sugar cookie.
$(Sugar) = \frac{5}{22}$

The probability of both events happening (selecting an oatmeal cookie and then a sugar cookie) is the product of the individual probabilities.
$(Oatmeal\, and\, Sugar) =(Oatmeal) \\times(Sugar)$

Plug in the values for the probability of selecting an oatmeal cookie and the probability of selecting a sugar cookie to calculate the probability of both events happening.
$(Oatmeal\, and\, Sugar) = \frac{7}{23} \\times \frac{5}{22}$