I don't like the blue ones, so because I'm that way, I culled those out and they're still sitting in front of me in a bowl. The rest I ate at my leisure—though rather less leisurely than is quite becoming, I'm afraid.At some point, near the end of the bag, I wondered what the probability was, if I pulled out two candies at random, that they'd have the same flavor. I looked at the candies that were in there, and it was a simple matter to figure the answer out. It was—ahh, but then I'd be giving the puzzle away.
I then turned to look away and puckishly reached into the bag and pulled out a pair of green apples. (Those are my second favorite, after the artificial grape ones, which, as you'll know if you eat them, taste nothing at all like actual grapes.) I wondered if that affected the probability at all—figuring that if anything, it would have reduced the odds—but after looking in and doing some quick figuring, I found that the odds were exactly the same as before.
"Hunh!" I thought to myself in surprise, and (if you know me at all, you know what happened next) I wondered what the odds were of that. As it so happens, that's not a question you can answer rigorously at all, without knowing the priors. But perhaps you can rigorously answer
Q1: What were the odds of drawing a matching pair of candies?
I reached in again, and this time pulled out a cherry and a grape; I did it again, and pulled out a matching pair of grapes. So this time, I thought, for sure there must be a change in the odds of drawing a match, but when I looked in again, the odds were once more exactly the same as the first time. What's more, I reached in again, pulled out a pair of green apples, looked in one last time, and the odds were again exactly the same as before!
Q2: Knowing there were no blue raspberry candies at all, how many of each of the other flavors were there, before I pulled out the first pair of green apples?
