Our lecturer was a man with great sense of humor, then Assoc. Prof. Fatih Canatan.
In probability theory there were abundant of interesting real life examples that would pull you out of the realm of photons (electromagnetic fields’ constituent particles) and put you on the ground standing firm on your feet, well almost firm, as we are talking about probabilities here. The theory of probability gave us the students a rare sense of belonging in our otherwise weird electrical engineering curriculum.
I remember we also had a classmate, an annoying type, you know the guy, a definitive 'nerd', who constantly asks stupid questions without giving a fig about how disruptive he is being for the class.
“Mmm. A null set is an empty set as I already mentioned number of times. For example you, you are a null set!”.
The whole class suddenly cracked up, tears in eyes.
A classical problem in introductory probability lectures is:
"What is the probability of finding at least two people with the same birthday in a group of people?"
Most people underestimates the value of such probability. To give you an idea in a group of 20 people the probability is 41%.
In my hand writing the solution is given as follows :
Wolfram Alpha is a magnificent online math tool. Go to http://www.wolframalpha.com then in the search box type;
1 - 365!/((365-k)!*365^k)
After a few seconds Wolfram will give you a set of interesting plots and numbers in various forms:
If you want to zoom into the probability distribution for a group size between 20 and say 40, simply follow your intuition:
1 - 365!/((365-k)!*365^k) from 20 to 40
And you would get this;
1 - 365!/((365-k)!*365^k) where k=40
And you would get the result as 89.1232%:
Isn’t this amazing! I mean the whole thing. It simply feels great NOT to be a null set.