Steven G
Elite Member
- Joined
- Dec 30, 2014
- Messages
- 14,397
Danielle, Lilliana, and Melody play a fighting video game in tournament mode. In this mode, two players play a match, and the winner of the match plays a new match against the player who was sitting out. This continues until a player wins two matches in a row. Danielle and Lilliana play the first match.
If they are all equally skilled at the game, then what is the probability that Melody will win the tournament?
Let's call the players D, L and M.
So D and L play and someone wins, say D.
So D and M plays. If D wins the tournament is over so M must win.
I claim that M must win the next round because if M loses (so L wins), then D and L plays. Whoever wins the D and L match won two matches and the tournament ends.
So, in the end M has to win two matches in a row which has a probability of 1/2 * 1/2 = 1/4.
My question is what is wrong with my logic/answer as 1/4 is not the correct answer?
If they are all equally skilled at the game, then what is the probability that Melody will win the tournament?
Let's call the players D, L and M.
So D and L play and someone wins, say D.
So D and M plays. If D wins the tournament is over so M must win.
I claim that M must win the next round because if M loses (so L wins), then D and L plays. Whoever wins the D and L match won two matches and the tournament ends.
So, in the end M has to win two matches in a row which has a probability of 1/2 * 1/2 = 1/4.
My question is what is wrong with my logic/answer as 1/4 is not the correct answer?
Last edited: