There are $N$ distinct types of coupons in a cereal boxe and each type, independent of prior selections, is equally likely to be in a box. You draw $M$ coupons from the cereal box. What is the expected probability that the $i$-th coupon type is not among the $M$ coupons?
I am confused about the prefix "expected" in this case. The probability in this situation isn't a random variable, and isn't it simply $$ \frac{(N - 1)^M}{N^M} $$ ?
Here's the exact problem from the book:
I already solved parts A and B. But in the hint for, the last sentence seems like a follow up question that needs to be solved, or maybe it's actually a hint for part B. I assumed it was a followup question.
You’re right on both counts – it should just be “probability”, not “expected probability”, and the desired probability is $\left(\frac{N-1}N\right)^M$.