Question

dante buys a bag of cookies that contains 5 chocolate chip cookies, 8 peanut butter cookies, 4 sugar cookies, and 7 oatmeal raisin cookies. what is the probability that dante randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects another chocolate chip cookie? (round your answer to 4 decimal places.)

Explanation:

Step1: Calculate total number of cookies

The total number of cookies initially is $5 + 8+4 + 7=24$.

Step2: Calculate probability of first - chocolate - chip selection

The probability of selecting a chocolate - chip cookie on the first draw is $P_1=\frac{5}{24}$.

Step3: Calculate number of cookies and chocolate - chip cookies after first draw

After eating one chocolate - chip cookie, the total number of cookies is $24 - 1=23$, and the number of chocolate - chip cookies is $5 - 1 = 4$.

Step4: Calculate probability of second - chocolate - chip selection

The probability of selecting a chocolate - chip cookie on the second draw, given that a chocolate - chip cookie was selected on the first draw, is $P_2=\frac{4}{23}$.

Step5: Calculate the joint probability

Since these are dependent events, the probability of both events occurring is $P = P_1\times P_2=\frac{5}{24}\times\frac{4}{23}=\frac{20}{552}\approx0.0362$.

Answer:

$0.0362$