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Monty Hall Problem

Decent Essays

Introduction-
Probability is the measure of the likeliness that an event will occur.
Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events. If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. The aim of this investigation is to solve a long-standing probability question; The Monty Hall problem. I chose this topic for a number of reasons. Firstly, we have just started studying probability in class and I enjoy learning and working ahead. …show more content…

An example of a conditional probability question would be as follows;
Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

While the obvious answer is ½ this is not true. Let us look at the possibilities possible:
Case 1- boy and boy
Case 2- boy and girl
Case 3- girl and boy
Case 4- girl and girl

As the problem states that Mr. Smith has 2 children one of whom is a boy, we case safely remove case 4. Hence the probability of both Mr. Smith’s children being boys is;
=(case 1)/(# of cases )
=1/3

The Monty Hall Problem-

The Monty Hall Problem’s origin is from the TV show, “Let’s Make A Deal” hosted by Monty Hall. The statement of the problem is as follows: “You are a contestant in a game show in which a prize is hidden behind one of three curtains. You will win the prize if you select the correct curtain. After you have picked one curtain but before the curtain is lifted, the emcee lifts one of the other curtains, revealing an empty stage, and asks if you would like to switch from your current selection to the remaining curtain. How will your chances change if you

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