Final answer:
The probability of selecting a cheesecake and then a cookie from 10 desserts involves multiplying the individual probabilities of selecting each, given there are both cheesecakes and cookies among the desserts.
Step-by-step explanation:
The question asks us to determine the probability of selecting a cheesecake, putting it back, and then selecting a cookie from a total of 10 desserts. Assuming there are cheesecakes and cookies in the mix, the probability of selecting a cheesecake first is based on how many cheesecakes there are out of 10. However, without the specific number of cheesecakes, we can't compute this probability. Let's denote the number of cheesecakes as C and the probability of selecting one as P(cheesecake) = C/10.
After returning the cheesecake, the total number of desserts is still 10. If there are cookies in the mix, that probability will depend on the number of cookies, denoted as K. The probability of then selecting a cookie is P(cookie) = K/10.
Since the selection is independent (the cheesecake is put back each time), the joint probability is simply the product of the two individual probabilities: P(cheesecake then cookie) = (C/10)*(K/10).