Monty Hall problem In Parade magazine, a reader posed the following question to Marilyn vos Savant and the "Ask Marilyn" column:
Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say $\# 1,$ and the host, who knows what's behind the doors, opens another door, say # $3,$ which has a goat. He says to you, "Do you want to pick door # $2 ?$ Is it to your advantage to switch your choice of doors? $^{4}$
The game show in question was Let's Make a Deal and the host was Monty Hall. Here's the first part of Marilyn's response: "Yes; you should switch. The first door has a $1 / 3$ chance of winning, but the second door has a $2 / 3$ chance." Thousands of readers wrote to Marilyn to disagree with her answer. But she held her ground.
(a) Use an online Let's Make a Deal applet to perform at least 50 repetitions of the simulation. Record whether you stay or switch (try to do each about half the time) and the outcome of each repetition.
(b) Do you agree with Marilyn or her readers? Explain.
Probability: What Are the Chances?
Randomness, Probability, and Simulation