kelly buys a bag of cookies that contains 5 chocolate chip cookies, 7 peanut butter cookies, 9 sugar cookies…
kelly buys a bag of cookies that contains 5 chocolate chip cookies, 7 peanut butter cookies, 9 sugar cookies and 8 oatmeal cookies.\nwhat is the probability that kelly reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie?\n\ngive your answer as a fraction, or accurate to at least 4 decimal places.
Answer
Explanation:
Step1: Calculate total number of cookies
The total number of cookies is $5 + 7+9 + 8=29$.
Step2: Calculate probability of first - selecting a chocolate chip cookie
The probability of selecting a chocolate chip cookie first is $\frac{5}{29}$ since there are 5 chocolate chip cookies out of 29 total cookies.
Step3: Calculate probability of second - selecting a sugar cookie
After eating one chocolate chip cookie, there are 28 cookies left. There are 9 sugar cookies, so the probability of selecting a sugar cookie second is $\frac{9}{28}$.
Step4: Calculate the combined probability
Since these are independent - like (in the sense of sequential selection) events, we multiply the probabilities of each event. The combined probability is $\frac{5}{29}\times\frac{9}{28}=\frac{45}{812}\approx0.0554$.
Answer:
$\frac{45}{812}\approx0.0554$