The Monty Hall problem is an interesting puzzle in probability which has a counter-intuitive answer. In fact, it is documented that many people got the answer wrong and many people continue to get the answer wrong. The problem The problem goes somewhat like this: Imagine a game show. There are 3 doors and behind one door there is a car and behind the other 2, goats. The player picks a door hoping to win a car that’s behind the door....
Life needs energy to survive. Energy is needed to perform basic life functions like movement, hunting and gathering, protecting from prey and natural elements. It is converted from one form to another. Eventually, the energy within the living organism is expelled from the organism while useful work is performed. Why and how energy for life? Work is done when there is change in energy. In other words, energy has to go somewhere, so work gets done....
I came across this probability problem and thought it was interesting. What is the expectation of distance (from the center) of a circular disc to uniformly distributed random points on the disc? If you pick a random point (or throw a dart) on a circle, there are more chances of the point landing somewhere between the center and the perimeter of the circular disc. Intuitively, this is because there are more points on the disc, i....