Eric’s mother wants to help him with his math homework. She puts 24 cookies in a cookie jar. Twelve of the cookies are chocolate chip, 8 are oatmeal, and 4 are peanut butter. She then has Eric select a cookie from the jar without looking. Next, without replacing the first cookie, Eric picks a second cookie without looking in the jar. What is the probability Eric will pick an oatmeal cookie first and a chocolate chip cookie second?
A. 1/6
B. 4/23
C. 5/6
D. 59/69
To find the probability of Eric picking an oatmeal cookie first and a chocolate chip cookie second, we need to calculate the probability for each event and then multiply them together.
First, let's calculate the probability of picking an oatmeal cookie first. There are a total of 24 cookies in the jar, and 8 of them are oatmeal cookies. Thus, the probability of selecting an oatmeal cookie first is 8/24, which simplifies to 1/3.
Next, since Eric does not replace the first cookie, there are now 23 cookies in the jar. Out of these, there are 12 chocolate chip cookies remaining. Therefore, the probability of selecting a chocolate chip cookie second is 12/23.
To find the probability of both events occurring together, we multiply the probabilities of each event:
P(Oatmeal first and Chocolate chip second) = P(Oatmeal first) * P(Chocolate chip second)
= 1/3 * 12/23
Calculating this expression gives us 12/69.
Therefore, the answer is not among the given options.