Welcome to the Math312 Game Show! Where Probability Helps You Win Stuff! The Gam

Question

Welcome to the Math312 Game Show! Where Probability Helps You Win Stuff!

The Game:
Suppose you're on a game show, and you're given the choice of 3 doors. Behind one door is a car, behind the others, goats. You start by choosing a door, say number 1, which remains closed for now. The game show host, who knows what's behind the doors, opens another door, say number 3, which reveals a goat. He says to you, "You've already chosen door number 1, now that I've shown you a goat behind door number 3, do you want to switch to door number 2? Or stay with you original choice of door number 1?" After you choose to stay or switch doors, they are opened to see if you won!

The Questions:

If the goal is to win the car, is it in your advantage to stick with your original choice of door number 1, or to switch to door number 2, after the host has already shown you one goat. Or is the probability of winning the same regardless of if you switch or not? JUSTIFY YOUR REASONING WITH SENTENCES.

And what specifically is the probability (as a percent) of winning for each of those scenarios?

Your original post is due Wednesday at 11:59pm, with a response to at least one peer due by Sunday at 11:59pm. In your peer response, be sure to provide some critical insight to either support, disagree, or raise additional questions with their post. There is no credit for late posts.

We'll discuss this game further as a class next week!

Explanation / Answer

When initial choice is made from the 3 available options, probability of winning the car = 1/3 = 33%

If we stick with the same door, the probability is not changing and hence, the probability of winning the car is 33%

But when asked if you want to switch choice, we have two choices remaining in front of you and then you are chosing from one of the two available options.

Then, the probability of winning is 1/2 = 0.5 = 50%

So, it is in you advantage to stick to door number 2 as the probability increases from 33% to 50%

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