Question

A New Car! Precalculus B Name: Date: It's 1963. You are a contestant on the popular new game show Let's Make a Deal, hosted by Monty Hall. In front of you are three closed doors, marked 1, 2, and 3. Monty Hall says, "Behind two of these doors is a goat. But behind one door is a new car! Which door do you choose?" You take a deep breath and choose a door, door 2. Your heart is pounding as you wait for Monty to open door 2, but instead he says, "I'm going to open a different door for you first." And he opens door 1. Behind it, you see a goat. So the car is behind either the door you chose, door 2, or the third door, door 3. "Now," Monty says to you, "do you want to change your mind? Or would you like to make a deal and stick with door 2?" 1. Would you change your mind? Why or why not? 2. Let's look at this closely. When the game started, when all the doors were closed, what was the probability (as a fraction) that the car was behind your door, door 2? 3. What is the probability, before the doors are opened, that the car is behind either door 1 or door 3? Keep in mind that probability of mutually exclusive events should add up to 1. 4. Once Monty Hall opens door 1 to reveal a goat behind it, what is the probability that the car is behind door 2, the one you selected? Hint: It is not 1/2!

          A New Car!
Precalculus B
Name: Date:
It's 1963. You are a contestant on the popular new game show Let's Make a Deal, hosted by Monty Hall. In front of you are three closed doors, marked 1, 2, and 3.
Monty Hall says, "Behind two of these doors is a goat. But behind one door is a new car! Which door do you choose?"
You take a deep breath and choose a door, door 2.
Your heart is pounding as you wait for Monty to open door 2, but instead he says, "I'm going to open a different door for you first." And he opens door 1. Behind it, you see a goat.
So the car is behind either the door you chose, door 2, or the third door, door 3.
"Now," Monty says to you, "do you want to change your mind? Or would you like to make a deal and stick with door 2?"
1. Would you change your mind? Why or why not?
2. Let's look at this closely. When the game started, when all the doors were closed, what was the probability (as a fraction) that the car was behind your door, door 2?
3. What is the probability, before the doors are opened, that the car is behind either door 1 or door 3? Keep in mind that probability of mutually exclusive events should add up to 1.
4. Once Monty Hall opens door 1 to reveal a goat behind it, what is the probability that the car is behind door 2, the one you selected? Hint: It is not 1/2!

$A New Car! Precalculus B Name: Date: It's 1963. You are a contestant on the popular new game show Let's Make a Deal, hosted by Monty Hall. In front of you are three closed doors, marked 1, 2, and 3. Monty Hall says, "Behind two of these doors is a goat. But behind one door is a new car! Which door do you choose?" You take a deep breath and choose a door, door 2. Your heart is pounding as you wait for Monty to open door 2, but instead he says, "I'm going to open a different door for you first." And he opens door 1. Behind it, you see a goat. So the car is behind either the door you chose, door 2, or the third door, door 3. "Now," Monty says to you, "do you want to change your mind? Or would you like to make a deal and stick with door 2?" 1. Would you change your mind? Why or why not? 2. Let's look at this closely. When the game started, when all the doors were closed, what was the probability (as a fraction) that the car was behind your door, door 2? 3. What is the probability, before the doors are opened, that the car is behind either door 1 or door 3? Keep in mind that probability of mutually exclusive events should add up to 1. 4. Once Monty Hall opens door 1 to reveal a goat behind it, what is the probability that the car is behind door 2, the one you selected? Hint: It is not 1/2!$

Added by Jameson L.

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