## Probability is deep.

October 19, 2012 § Leave a comment

I find “probability” interesting in the past few years.

If I’m about to ask some embarrassing questionts to you and your mates directly, you all obviously do not asnwer to me.

Let the embarrassing question be “Have you ever cheated on someone?” (although probably this is not that embarrassing unless you are surrounded by your ex-es.)

There is a way to find out a rough estimation for the number of you who have cheated on someone!

If I say to you “Ok, I’ll give you a coin to toss. If EITHER coin shows heads OR you’ve cheated on someone, raise your hands,” you’d feel a lot more comfortable answering the questions.

Ok, 6 out of 10 of you raised the hands.

Let X be the number of people who have cheated on someone before. Let’s call it group C.

The probability of coin toss showing heads is 0.5, therefore, the number of people whose coin showing heads is 5, group H.

Here is the tricky bit – bear in mind that there are some people with coin showing heads AND ALSO cheated on someone before. In a word, there’s an overlapping area between group C and group H if you imagine the Venn diagram.

The probability for those people would be; X/2

because no matter if you have cheated on someone or not, the probablity of getting the coin heads is 0.5.

Since X is 6, 6/2 is 3.

6 – 3 =3

Hence, I can estimate the number of people who have cheated on someone before is 3.

Of course, there are some critisisms about the whole process of finding the estimation using this method.

You might argue it is not always the case that a coin shows heads and tails equally. You might say “It is underestimating that exactly 5 people will toss a coin and gain heads.”

Sure, you are right…

However, we can say “the probability of coin toss showing heads is 0.5” confidently, while we are uncertain of the probability of people cheating on someone.

To make it clear, let’s put it this way;

We sacrifice the risk of uncertainty in coin toss in order to eliminate the uncertainty of not getting accurate answers.

In addition, the example had only 10 people in total, but as the number of candidates increases, the certainty of estimation increases. This is called; Law of large numbers.

Finally, I’d like to conclude – probability is deep…