(Monty Hall problem) In the television game show Let's Make a Deal, the room is equipped with th

1. Initially, you have a 1/3 chance of choosing the car and a 2/3 chance of choosing a goat.

Question

(Monty Hall problem) In the television game show Let's Make a Deal, the room is equipped with three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, the host, who knows what's behind the doors, opens one of the other two doors, revealing a goat, and asks you if you wish to switch to the third door. A. Find out the probability of winning the car if you stick with door 1. B. Find out the probability of winning the car if you switch. C. Should you change your selection?

          (Monty Hall problem) In the television game show Let's Make a Deal, the room is equipped with three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, the host, who knows what's behind the doors, opens one of the other two doors, revealing a goat, and asks you if you wish to switch to the third door.
A. Find out the probability of winning the car if you stick with door 1.
B. Find out the probability of winning the car if you switch.
C. Should you change your selection?

(Monty Hall problem) In the television game show Let's Make a Deal, the room is equipped with three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, the host, who knows what's behind the doors, opens one of the other two doors, revealing a goat, and asks you if you wish to switch to the third door.
A. Find out the probability of winning the car if you stick with door 1.
B. Find out the probability of winning the car if you switch.
C. Should you change your selection?

Added by Jose Miguel S.

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