probability puzzles
| medium | probability |
A and B are in a team called AB, playing against C. If AB team wins they win Rs 3, nothing otherwise.
The Game: A and B are placed in 2 separate rooms far away. A will toss a coin and B will also toss a coin; A will have to guess the outcome of B's toss and B will guess A's. If both guesses are right, team AB wins Rs 3, nothing otherwise. Should they play the game, by paying Rs 1 at the start?
The winning probability is not 1/4. They can make a strategy before the game.
1/2
Let's list down all the possibilities.
| A | B |
|---|---|
| H | H |
| H | T |
| T | H |
| T | T |
Observe that out of times, their coins have the same face, i.e. either both heads or both tails.
They can speak their own coin's face as their guess. They win the game with a probability of .
The pay-off will be positive (), and hence they should play this game.