WILL CHILDREN OF A FAMILY SHARE THE SAME BIRTH DAY?

ADVT: SMARTWATCHES IN AMAZON

Suppose, a family has two or three children. Will they have the same birthday? It happened in Great Briton. In 2010, Jennifer and Briss Allah were expecting their third child. They were also preparing to celebrate the birthday of their two children, Adam and Najla on 7th October.

While Mum Jennifer was blowing up balloons for the upcoming celebrations, she felt something in her stomach and realized that her contractions had begun. She could not believe it. The unthinkable was about to happen. The family's third child, Sami, was also born on 7th October. The "daily mail" proclaimed,' Happy birthday to you ... and you... and you too. Couple's three children born on the same date'.

An event such as this occurring is mindboggling. But statistically, it can happen. Let us see the little math behind it.

The probability of first

child born on any day = 1

The probability of the second

child born on same day =1*1/365

The probability of third

child born on the same day too =1*1/365*1/365=1/133225

That is, the chance for a family to have three children born with the same birthday is 1 in 133225.

Remember, A chance for getting a head in a coin toss is 1 in 2 or 1/2. If you toss a coin 10 times, you will get 5 heads.

That is 10*1/2 =5

similarly,

In the UK, there are around a million families with three children under eighteen, hence,

1 million *1/133225=7.5

We can expect around seven of these families to have all three children share the same birthday. On an individual level, we often think about how unlikely it would happen to us. "But with a large enough sample, any outrageous thing is likely to happen".

This example once again proves that, in the case of large numbers, any miracle can happen.

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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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