Two ancient philosophers, Lumpy and Eddie, were sitting on rocks flipping coins.

Lumpy and Eddie wondered about the probability of obtaining both a head and a tail. Here is how it went:

Eddie argued the following: “Look Lumpy, it’s clear to me that when we flip two coins, we should get one of each about half the time because there are two possibilities: They’re either the same or different.” Lumpy, on the other hand, argued this way: “Eddie, stop being a wise guy! If we flipped two coins, we should expect both a head and tail to come up about a third of the time because there are only three possibilities: two heads, two tails, and one of each.”

Which, if any, of these two guys is right? Is there another answer?

Next Lumpy and Eddie threw a third coin in the mix and wondered about the probability of obtaining 2 heads and a tail or 2 tails and a head.
(a)
What would Lumpy say in this case?
(b)
What would Eddie say in this case?

Be sure to clearly explain why you think they would answer in the way you suggest.

2024-10-10 13:39:00