CALCULATE YOUR WAITING IN A QUEUE

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.

Comments

THE EARTH, A SUPER ORGANISM

JOIN MY COURSE: "Become a programmer in a day with python" A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess. It says, "Earth is a self-regulating organism like a human being. The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment". Hence the earth is still suitable for the life to thrive. Imagine, in a particular place, there are lot of flowers. Some flowers are white and some are darkly coloured. We know, white reflects light and heat while dark absorbs the same. White flowers can thrive in hot climate. But dark flowers requires cold climate. The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist. This is the essence of "Gaia" theory. On our earth, the oxygen constitute 20% of the atmosphere. The oxygen level is always mai

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

DISORDER IS THE "ORDER OF THE DAY"

Imagine a balloon full of air. The air molecules are moving randomly inside the balloon. Let us pierce the balloon with a pin. The air rushes out. Why should not the air molecules stay inside the balloon safely and ignore the little hole? That is not the way the world works. The molecules always "want to occupy as many states as possible". Hence the air goes out in the open to occupy more volume. The things always goes into disorder (entropy) and the disorder increases with time. The above statement is what we call "second law of thermodynamics". Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze. Freezing means bringing things to order and arrangement. It violates the second law. Hence it will never happen. Hence heat must flow from high temperature to low temperature and not the other way. The air molecules in y

sciencecapsules

Search This Blog