Question

furnell buys a bag of cookies that contains 6 chocolate chip cookies, 8 peanut butter cookies, 6 sugar cookies, and 4 oatmeal cookies. what is the probability that furnell randomly selects an oatmeal cookie from the bag, eats it, then randomly selects a peanut butter cookie?
probability = (round your answer to 4 decimal places.)

Explanation:

Step1: Calculate total number of cookies

Total number of cookies = 6 + 8+6 + 4=24

Step2: Calculate probability of selecting an oatmeal cookie first

Probability of selecting an oatmeal cookie, $P(O)=\frac{4}{24}$

Step3: Calculate number of cookies left after eating an oatmeal cookie

After eating an oatmeal cookie, number of cookies left = 24 - 1=23

Step4: Calculate probability of selecting a peanut - butter cookie second

Probability of selecting a peanut - butter cookie, $P(PB)=\frac{8}{23}$

Step5: Calculate the joint probability

Since the two events are dependent, the probability of both events occurring is $P = P(O)\times P(PB)=\frac{4}{24}\times\frac{8}{23}$
$P=\frac{32}{552}\approx0.0580$

Answer:

0.0580