Question

4.3 conditional probability. multiplication rule. rippy buys a bag of cookies that contains 4 chocolate chip cookies, 4 peanut butter cookies, 6 sugar cookies and 8 oatmeal raisin cookies. what is the probability that rippy randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects another chocolate chip cookie? write as a fraction. probability = enter a fraction or integer (no mixed numbers)

Explanation:

Step1: Calculate total number of cookies

The total number of cookies is $4 + 4+6 + 8=22$.

Step2: Calculate first - draw probability

The probability of selecting a chocolate - chip cookie on the first draw is $\frac{4}{22}=\frac{2}{11}$ since there are 4 chocolate - chip cookies out of 22 total cookies.

Step3: Calculate second - draw probability

After eating one chocolate - chip cookie, there are 3 chocolate - chip cookies left and 21 total cookies left. So the probability of selecting a chocolate - chip cookie on the second draw is $\frac{3}{21}=\frac{1}{7}$.

Step4: Use multiplication rule

By the multiplication rule for dependent events, the probability of both events occurring is the product of their probabilities. So the probability is $\frac{2}{11}\times\frac{1}{7}=\frac{2}{77}$.

Answer:

$\frac{2}{77}$