FALSE POSITIVE AND DISEASE

In tossing coin, each event (toss) is independent event. The outcome of one toss does not influence the next toss. Hence the chance of getting a head is always 1/2.
Suppose, you left your car key in one of the four rooms of your apartment. Let us name the rooms as A,B,C and D. The probability of finding the key in the room A is 1/4. That is written as P(A) =1/4.
You searched the room A thoroughly and failed to find the key. Now the probability of finding the key in the room B is 1/3. It is written as P(B/A)=1/3. It is read as "probability of B given A". Remember the symbol.

A new disease has stroked the people. But only one (1%) of the people is affected by that disease. A Scientific lab has made a new 'device and kit' which detects the disease with 98% accuracy. But there is a catch. If a person does not have the disease, the device will falsely recognize the disease with 2% chance. It is a 'false positive'. 98% accuracy seems to be good for us. But let us see, how the story goes

P(A) - probability of population having disease = 1% = 0.01
P(B)- probability of population having No disease = 99% = 0.99
P(C/A) - probability of disease detected in affected population = 98%=0.98
P(C/B) - probability of disease detected (falsely) in normal population 2%=.02
we want:
P(A/C) = probability of affected population really detected by the device.

In statistics, Bayes theorem states that
P(A/C) = P(C/A)*P(A)/(P(C/A)*P(A) +P(C/B)*P(B))
P(A/C) = 0.98*0.01/(0.98*0.01+0.02*0.99)=33.1%

Hence the device's accuracy has gone down from 98% to 33%. What happened? The disease is so rare. If you test the general public , the number of people not having the disease will greatly out number the small group that has it. So even a very low rate of false positives will strongly impact the overall results.
Bayes' theorem is very intriguing statistical tool. It has many interesting and important applications.
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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

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