Probability and
risk management are involved in everything that we do. They make up the science of chance. I am currently taking a course here at Penn
State on Probability Theory and it has really sparked my interest. The basic concept of probability lies in the
likelihood of an occurrence of an event.
In class, for example, events can be categorized as event A and event A'. This is an example of a binomial distribution
of events. Since there is no third
outcome, the probability of event A occurring is equal to the probability of
event A' not occurring.

Many times we are
torn between the choice to do something or to not do something. This would be considered a real-life binomial
distribution of chance. It is the most
common type of distribution in our day-to-day lives and one of the more simple
to understand. The risk management part
comes in when there is a reward involved with the occurrence. In a sense, the analysis of risk is weighing
your options. In our lives the
probability of an event corresponds to the risks and rewards we place on a
decision.

Perhaps this
decision is whether to go out or stay in and catch up on work. Lets say that event A is going out and event
A' is to not. On a Monday, there is very
little reward for event A being that there won't be as many people going out as
there would be on a weekend night.
During the weekend, there is a higher reward for event A since you will
have more fun being around more of your friends than during the week. These are the rewards of going out relative
to the day of the week. The risks
associated with these days are inversely related to the rewards. To go out means to lose the opportunity to
study and we determine the probability of event A occurring based on the reward
of choice A.

In class we
learned that due to the Law of Large Numbers probability would determine the
choice we should make in the future. In
the long run, the choice will waver towards whatever event has the highest
probability.

In Science 200,
we spoke about the game show problem from Let's Make A Deal. The decision at first was to pick one of
three doors in hopes of getting the reward (event A) of a new car behind one
door and not a goat (event A') behind two of the doors. The probability at first is simply one
(reward) out of three choices. This is a
33% and there was very little disputing it.

After a choice
was made, one of the other two doors was opened to reveal a goat. Following the unveiling of a goat,
contestants were offered the chance to switch doors. This choice at first appeared to be a 50/50
shot at a new car and many quickly dismissed statistics and probability. Instead they thought with their hearts rather
than brains. The stubbornness of many
contestants to stick to their guns and keep the first door resulted in often
times, a goat.

Over time a trend
began to occur in which the decision to stay resulted in a 33% chance of reward
and not a 50% chance that was assumed.
The Law of Large Numbers dismisses bad luck in this situation and
statisticians looked for a true reason behind the probability. It was first proposed by Steve Selvin in a
letter to the American Statistician that the correct choice was to switch
doors. This was because the game show
host knew which door the car is behind and he knew to pick the door with the
goat in it to display to you. At first
the probability of your door having a car was 33% (event A) and a 67% chance
that the car was behind the other two doors (event A'). Since the host eliminated half of the doors
from the probability of A' the full probability landed on the door which he did
not display. The door that you chose at
first maintained its original probability while the other door doubled its
chances on winning. This image captures the probability of winning given that you switch doors:

Looking at it now
it seems like a no brainer to switch doors and take the two thirds odds. This concept is not easily grasped and led to
debate over the topic but in the end, you can't argue with the science
involved. Probability is all around us
and is something that should be taken advantage of with our every day
decision-making.

BBC Article Explanation

http://www.bbc.co.uk/news/magazine-24045598

Demonstration of the Monty Hall Problem

http://www.youtube.com/watch?v=mhlc7peGlGg

Statistical Proof of the Monty Hall Problem

When I first heard about this, I was so confused and my immediate answer to the problem was: stick with the door with you have. It's done pretty well so far, so why not just stick with it to the end? Looking at this now it seems to easy to win and yet , ignoring the 1/3 chance of failure, there is one other major factor that stands in our way of winning: Human nature.

Like Andrew said in class humans are averse to taking responsibility for their actions when they have negative consequences so it's possible that someone might go in to the show and even though they know of this may choose not to switch doors, simply because in case they choose wrongly, they won't be to blame, strange isn't it?

On a side note, I read this interesting paper that shows the possibility of two alternate variations of the Monty Hall problem. I especially liked the Monty Fall problem!