Question

esmeralda buys a bag of cookies that contains 7 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 8 oatmeal cookies. what is the probability that esmeralda randomly selects a sugar cookie from the bag, eats it, then randomly selects a peanut butter cookie? write as a fraction.
probability =
basic
$\frac{n}{square}$ $\frac{square}{square}$ $infty$ dne
enter a fraction or integer (no mixed numbers) more..

Explanation:

Step1: Calculate total number of cookies

$7 + 6+6 + 8=27$

Step2: Calculate probability of selecting a sugar - cookie first

The number of sugar cookies is 6. So the probability of selecting a sugar cookie, $P(S)=\frac{6}{27}$

Step3: Calculate probability of selecting a peanut - butter cookie second

After eating a sugar cookie, there are 26 cookies left. The number of peanut - butter cookies is 6. So the probability of selecting a peanut - butter cookie given a sugar cookie was eaten first, $P(PB)=\frac{6}{26}$

Step4: Calculate the combined probability

By the multiplication rule for dependent events, $P = P(S)\times P(PB)=\frac{6}{27}\times\frac{6}{26}=\frac{36}{702}=\frac{2}{39}$

Answer:

$\frac{2}{39}$