Tammy's mom is baking cookies for a bake sale. Currently, there are 22 chocolate chip cookies, 18 sugar cookies, and 15 oatmeal cookies on the counter. Tammy sneaks into the kitchen, grabs a cookie at random, and eats it. Five minutes later, she does the same thing with another cookie. What is the probability that neither of the cookies is a chocolate chip cookie?
So you want 2 consecutive non-chocolate cookies, there are 33 out of the total of 55 cookies
prob of that = (33/55)(32/54) = 16/45
Well, let's use our cookie-culating skills to find out the probability!
First, we need to know the total number of cookies on the counter. So, if we add up the chocolate chip, sugar, and oatmeal cookies, we get 22 + 18 + 15 = 55 cookies.
Now, let's calculate the probability of not getting a chocolate chip cookie on the first grab. We want to find the number of non-chocolate chip cookies (18 sugar + 15 oatmeal = 33 cookies) divided by the total number of cookies (55). So, the probability of not getting a chocolate chip cookie on the first grab is 33/55.
Since Tammy eats the first cookie, there are now 54 cookies left on the counter. Similarly, we want to find the probability of not getting a chocolate chip cookie on the second grab, given that the first cookie was not a chocolate chip cookie. So, we have to recalculate the number of non-chocolate chip cookies (17 sugar + 15 oatmeal = 32 cookies) divided by the new total number of cookies (54). Therefore, the probability of not getting a chocolate chip cookie on the second grab is 32/54.
To find the probability that neither of the cookies is a chocolate chip cookie, we multiply the probabilities of both events happening. So, the probability is (33/55) * (32/54) ≈ 0.3207, or about 32.07%.
So, there you have it! The probability that Tammy doesn't get a chocolate chip cookie on either grab is approximately 32.07%. I hope that brings a smile to your face, just like the thought of delicious cookies!
To find the probability that neither of the cookies Tammy eats is a chocolate chip cookie, we need to calculate the probability of choosing a non-chocolate chip cookie for each cookie Tammy eats.
Step 1: Calculate the total number of cookies.
The total number of cookies on the counter is: 22 + 18 + 15 = 55 cookies.
Step 2: Calculate the probability of choosing a chocolate chip cookie on the first cookie Tammy eats.
The probability of choosing a chocolate chip cookie on the first try is: (number of chocolate chip cookies) / (total number of cookies) = 22 / 55.
Step 3: Calculate the probability of choosing a non-chocolate chip cookie on the first cookie Tammy eats.
The probability of choosing a non-chocolate chip cookie on the first try is: 1 - (probability of choosing a chocolate chip cookie) = 1 - (22 / 55) = 33 / 55.
Step 4: Calculate the probability of choosing a chocolate chip cookie on the second cookie Tammy eats.
After Tammy has eaten one cookie, there are now 54 cookies left.
The probability of choosing a chocolate chip cookie on the second try is: (number of chocolate chip cookies left) / (total number of cookies left) = (22 - 1) / (55 - 1) = 21 / 54.
Step 5: Calculate the probability of choosing a non-chocolate chip cookie on the second cookie Tammy eats.
The probability of choosing a non-chocolate chip cookie on the second try is: 1 - (probability of choosing a chocolate chip cookie on the second try) = 1 - (21 / 54) = 33 / 54.
Step 6: Multiply the probabilities of choosing a non-chocolate chip cookie on both the first and second try.
To find the probability that neither of the cookies Tammy eats is a chocolate chip cookie, we need to multiply the probabilities from step 3 and step 5: (33 / 55) * (33 / 54) = 1089 / 2970.
Therefore, the probability that neither of the cookies Tammy eats is a chocolate chip cookie is 1089 / 2970.
To find the probability that neither of the cookies Tammy eats is a chocolate chip cookie, we first need to determine the total number of cookies available after Tammy eats the first one.
Initially, there are 22 chocolate chip cookies, 18 sugar cookies, and 15 oatmeal cookies, making a total of 55 cookies on the counter.
After Tammy eats the first cookie, there are now 54 cookies left. The number of chocolate chip cookies has decreased by 1, but the numbers of sugar and oatmeal cookies remain the same.
Now, Tammy proceeds to eat another cookie, so the remaining number of cookies becomes 53. The numbers of chocolate chip, sugar, and oatmeal cookies decrease accordingly.
To calculate the probability of Tammy not choosing a chocolate chip cookie for either of the two cookies she eats, we need to consider the updated numbers of chocolate chip, sugar, and oatmeal cookies.
So, after Tammy eats the first cookie, the number of chocolate chip cookies becomes 22 - 1 = 21.
And after she eats the second cookie, the number of chocolate chip cookies becomes 21 - 1 = 20.
The probability of Tammy not choosing a chocolate chip cookie for the first cookie is given by the ratio of the number of non-chocolate chip cookies to the total number of remaining cookies:
P(not choosing a chocolate chip cookie for the first cookie) = (18 + 15)/(54) = 33/54.
When Tammy picks the second cookie, the probability of not choosing a chocolate chip cookie is given by the ratio of the updated number of non-chocolate chip cookies to the new total number of remaining cookies:
P(not choosing a chocolate chip cookie for the second cookie) = (18 + 15)/(53) = 33/53.
To calculate the probability of both events happening (Tammy not choosing a chocolate chip cookie for either of the two cookies she eats), we multiply the probabilities of each event:
P(neither cookie is a chocolate chip cookie) = P(not choosing a chocolate chip cookie for the first cookie) * P(not choosing a chocolate chip cookie for the second cookie)
= (33/54) * (33/53)
Hence, the probability that neither of the cookies is a chocolate chip cookie is (33/54) * (33/53).