PREJUDICE AND MINORITIES

The minorities seem to undergo some troubles in an office, in a class, in a town or in a country. Let us try to find out the truth. In every class or category of population, there may be 10% of troublemakers. Let us explore with an example.

There are 100 staff in an office. 90% of them are right handers (write with right hand). 10% of each category blame the others for mistakes in writing work. 10% of 90 persons is 9. Hence 9 persons will blame the minority 10 left handers. Most probably each day one left hander will be in trouble. But 10% of 10 is 1. Hence, just one left hander is there to blame all 90 right handers. On average, a right hander would go two years without being abused by a lefty. Equal percentage of abusers are there in each category. But it seems that, minority is affected a lot. There is a formula to measure the abuse.

The expected number of abusive incidents one group receives = other population * other population's rate of prejudice/ your population.
IN THE CASE OF LEFTIES
=90*10%/10 = 90*0.1/10
=9/10 =0.9
nearly one incident will take place (abusing lefthanders) in a period.
In the case of right handers:
=10*0.1/90
=1/90=0.01

There is a 0.01 chance for the right hander to get abused by the left handers. The formula clearly tells that the chance for abusive incident for right handers is very, very less.
How to improve the office atmosphere? We can employ more left handers, that is one way. But the real solution is to reduce the prejudice rate and for everyone to see the merits in other hand.
This principle can be employed in the case of gender differences, skin colour differences etc.

WHY WE HAVE SEGREGATED NEIGHBOUR HOOD?
Most of us are warm and friendly to others, regardless of skin colour or religious beliefs. But somehow our preferences led to segregated communities.
In a neighborhood, each group is perfectly happy so long as at least one in three of their immediate neighbors is like them. They like diversity, but if they feel heavily outnumbered, they move elsewhere... and before long, the community get segregated due to 'preference'. Hence, there is nobody to blame for segregation.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

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

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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