In the Monty Hall game, a contestant is shown three doors. Two of the doors have goats behind them and one has a car. The contestant chooses a door. Before opening the chosen door, Monty Hall opens a ...In the Monty Hall game, a contestant is shown three doors. Two of the doors have goats behind them and one has a car. The contestant chooses a door. Before opening the chosen door, Monty Hall opens a door that has a goat behind it. The contestant can then switch to the other unopened door, or stay with the original choice.
For a complete solution of the Monty Hall problem, we want to compute the conditional probability that the player wins, given that the host opens a door with a goat behind it: \[ \P(Y = U \mid V \ne U...For a complete solution of the Monty Hall problem, we want to compute the conditional probability that the player wins, given that the host opens a door with a goat behind it: \P(Y=U∣V≠U)=\P(Y=U)\P(V≠U) With the basic host and player strategies, the numerator, the probability of winning, has been computed.
