What is the probability of getting an odd number in a dice throw? There are three odd numbers 1,3 and 5. Hence the probability is 3/6=50%.
Draw a circle within a square
Drop pins randomly in the square. The pin should fall on its tip. What is the chance of pin falling within the circle?
Area of the square = 2r*2r= 4r^2.
Area of the circle = pi r^2.
Hence the chance of a pin falling in the circle = area of the circle/area of the square.
= pi*r^2/4*r^2
= pi/4 = 3.14/4 = 0.7854
=78.54%
Hence the pin mostly will fall within the circle.
Let us assume that you are waiting in a queue in the doctor's clinic for treatment. Let us further assume that the waiting time varies between 0 to 45 minutes and the treatment time varies between 0 to 30 minutes . What is your chance of getting out of the clinic in 30 minutes? Let us name the waiting time as X and the treatment time as Y, then plot a graph.
We get a rectangle. Your time X and Y may fall at any point in the rectangle. Now what is your chance of total time not exceeding 30 minutes?
That is, X+Y must be less than 30.
Draw a line for the equation X+Y = 30 in the same graph. Any point in the shaded region below the line satisfies your condition.Now what is the chance to meet our condition?
The chance = Area of the shaded triangle/ area of the rectangle.
=0.5*b*h/l*b
=0.5*30*30/30*45
= 450/1350 = 0.33333
= 33.33%
So the chance is 33% which is not much. You should be prepared to wait for a longer time.
Here the probability and geometry is combined. These kind of problems can be solved using geometry. So statistics gives measurement for our expectations.