Exercise 3.26
David
"We don't know if the first book that was drawn was a fiction hardcover or a fiction softcover. So I am confused on how we would know how many hardcovers are left after the first draw."
This is *exactly* right, and to be honest, being able to articulate this ambiguity is the hardest part, so you're well on your way to solving this problem. I'll just give you a hint.
When you encounter an ambiguity like this, try to break the problem down based on the ambiguity. In this case, you've identified that the outcome can occur in exactly one of two scenarios, so let's rephrase the probability to align with those two scenarios in our notation:
P(1st is fiction, 2nd is hardcover)
= P((1st is a fiction paperback, 2nd is hardcover) OR (1st is a fiction hardcover, 2nd is hardcover))
This is not a huge hint, but hopefully it's enough to get you unstuck! As I'd mentioned earlier, you have already done the hard part by articulating the possible scenarios. I'm only putting that into a bit more formal probability notation.
Good luck!
Cheers,
David
Jennifer1977
Hi,
I am stumped by Exercise 3.26 in the Third Edition.
Part (a) makes sense to me - what is the probability of a hardcover book being drawn first and then a paperback fiction book being drawn second, because these two groups are mutually exclusive.
However, I don't know how to calculate the answer to (b) - if a fiction book is drawn first, how do we figure out the probability of a hardcover book being drawn second? We don't know if the first book that was drawn was a fiction hardcover or a fiction softcover. So I am confused on how we would know how many hardcovers are left after the first draw.
Thank you!