There are 4 chocolate chip cookies and 12 oatmeal cookies in a jar. If you reach in an randomly choose 2 cookies without replacing the first, what is the probability that both will be chocolate chip?
To find the probability, we need to know the total number of cookies and the number of chocolate chip cookies.
The total number of cookies can be found by adding the number of chocolate chip cookies and the number of oatmeal cookies: 4 + 12 = 16.
Next, we need to calculate the probability of choosing a chocolate chip cookie on the first draw. Since there are 4 chocolate chip cookies out of a total of 16 cookies, the probability of choosing a chocolate chip cookie on the first draw is 4/16.
After the first cookie is drawn without replacement, there will be 3 chocolate chip cookies left out of a total of 15 remaining cookies.
So, the probability of choosing a chocolate chip cookie on the second draw, given that the first cookie was a chocolate chip cookie and was not replaced, is 3/15.
Finally, to find the probability of both cookies being chocolate chip, we multiply the probabilities of each draw. Therefore, the probability is (4/16) * (3/15) = 12/240 = 1/20.
Therefore, the probability that both cookies will be chocolate chip is 1/20.