To find the probability of Kimberly randomly selecting a chocolate chip cookie from the bag, eating it, and then randomly selecting another chocolate chip cookie, we'll calculate it step by step:
Step 1: Probability of selecting a chocolate chip cookie on the first draw.
There are a total of 7 chocolate chip cookies in the bag, and the bag contains a total of (7 + 9 + 5 + 6) = 27 cookies.
Probability of selecting a chocolate chip cookie on the first draw = Number of chocolate chip cookies / Total number of cookies = 7 / 27.
Step 2: Probability of selecting a chocolate chip cookie on the second draw after eating one.
After eating one chocolate chip cookie, there are 6 chocolate chip cookies remaining, and there are (27 - 1) = 26 cookies left in the bag.
Probability of selecting a chocolate chip cookie on the second draw = Number of remaining chocolate chip cookies / Total number of remaining cookies = 6 / 26.
Step 3: Probability of both events happening (independent events).
Since the two draws are independent events (eating one cookie does not affect the next draw), we can multiply the probabilities of both events to find the overall probability.
Overall probability = Probability of step 1 * Probability of step 2
Overall probability = (7 / 27) * (6 / 26)
Overall probability ≈ 0.0463
So, the probability that Kimberly randomly selects a chocolate chip cookie from the bag, eats it, and then randomly selects another chocolate chip cookie is approximately 0.0463 or 4.63%.