IS GUESSING IN EXAMINATION OK?

Toss a coin 100 times. You are likely to get head around 50 times. So there is a 50 % chance of getting a head or a tail. In other words, the probability of getting a head or a tail is 1/2. The range of probability is 0 (no chance) to 1(100% chance).

Suppose you toss a coin 3 times, what is the chance of getting a head in all the 3 throws. Here the multiplication rule comes to our help. This rule can be applied when the events are independent of each other. Just multiply the probability of the event 3 times.

total probability = 1/2*1/2*1/2=(1/2)^3 = 1/8 = 0.125

The probability of getting only heads 3 times consecutively is 1/8 or 1 in 8. That is , if 8 persons throw the coins 3 times, 'one' may get the head all the three times.

Let us assume that in a multiple choice question, there are 4 choices and one among them is correct. Guessing that correct answer has a chance of 1/4. If there are 10 questions, what is the probability of guessing all the answers right. We know by applying multiplication rule it is (1/4)^10 = 0.0000009536.

By taking reverse,
1/0.0000009536 = 104857

The chance is 1 in 100000. It means, if 100000 students write the 10 questions test, one may get all the answers right by guessing and not applying the knowledge. Hence the examination board is taking a safe bet.
That is why only three tries are allowed in a bank website for entering the password.
So do not take chance, use wisdom.

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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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