sciencecapsules

         How they measure chance? what are the basic operations in probability? Let us find out.       In tossing of a coin, there are two events-- head and tail.  The chance one event occurring = one/total number of events.  That is 1/2.  You have 50% chance of getting head or tail for each toss.  If you toss a coin, one time you should get head and next time you should get tail, so the formula says.  But both the times, you may get head or tail.  If you toss the coin 100 times, roughly 50 times you will get head and tail.  On the long run, the formula proves correct.     On throwing dice, there are six events (1,2,3,4,5,6).  Hence chance of getting an 'event' for a throw is 1/6.  There are three important logical operations in probability.  Let us go for it.   OR operation:     What is the chance or probability getting 1 or 6 in a roll.  Here, either 1 or 6 will do for us.      Probability  of getting 1 is 1/6      probability of getting 6 is 1/6 Now add both  1

1. Add two numbers        2+2 = 4 2. Add the number repeatedly      4+4 +4 = 12   3*4 = 12 That is multiplication 3. Now multiply repeatedly       12*12*12 = 1728  12ˆ3 = 1728     That is taking power     Let us go backwards. 1. Take cube root of 1728, we get 12                      (dividing repeatedly) 2. Divide 12 by 3, we get 4                         (subtracting repeatedly) 3. Subtract 2 from 4, we get 2  Addition is the basic operation, in moving forward.  But subtraction is the basic operation when moving backward.      Using addition and subtraction, we can move to and fro in mathematical process and get the desired answers. Calculus designed in similar fashion.     As an example consider a freely falling body.  We know the acceleration is 9.8 m /sˆ2 1. Acceleration= g = 9.8 m/sˆ2     if we integrate acceleration with respect to time,  2. we get  gt   Velocity of freely falling body.   If we further integrate velocity with respect to time.  3. we

         Whenever we wait for the city buses, they do not turn up for a long time or they come in groups of 3 or 4.  Why this happens?   Say, buses in a particular route are scheduled to arrive at a 'stop' for every 12 minutes.  That is, 5 buses are expected in a bus-stop in an hour.  But they are bunched up or scattered away due to heavy traffic or other odd reasons.  But there is a statistical formula (exponential distribution) using which, we can calculate our 'chance' of getting  a bus in an interval of time.       P = 1-eˆ(-rk) P- probability or chance of occurrence of event in the interval of time 0 sec to k second.     e- 2.71 ... Euler's constant.     r - rate of occurrence of events  In our case;  k = 5 minutes  r = 1/12:   one bus arrives for every 12 minutes. or 1/12 of a bus arrives at every minute. Now p = 1- 2.71 ˆ[-5(1/12)]             = 1-2.71 ˆ[-5/12]             = 1- 1/ 2.71 ˆ5/12             = 1-0.66  or 34 / 100 = 34% Hence o

          If you toss a coin 5 times, 4 times you may get head and one time you may get tail.  Toss it 10 times, it may be head 7 times or 3 times tail.  Toss it 100 times. Roughly 50 times you will get head or tail.  If you do 10000 times, Most likely 5000 times we get head or tail.  A computer can easily simulate this process.  As the 'number' increases, we reach the fifty percent probability. 7/10 is not 50%  But 5007/10000 is.      Let us roll the dice three times, it may be 2,4,6.  The average is 2+4+6/3 =4.  But, if we roll the dice many, many times and find the average, it will settle down exactly at 3.5.   1,1,2,3,5,8,13....144,233....      The above is the Fibonacci series, Adding the previous two numbers, you get the next number.  Now take successive numbers one by one and find their ratio.     2/1 = 2     3/2 = 1.5     5/3 = 1.666     8/5=1.6   13/8 = 1.625  21/13 = 1.615...  233/144 = 1.6180  377/233 = 1.6180...   On the long run, the ratio settles

       In a land line, voice is converted into electrical signals by a microphone and sent through wire.  The sound is reproduced by the speaker at the other end.  Now we have modern technology called fiber optics.  Here voice or digital data is first converted into electrical signals and then into light signals(laser or infra red) using electronic element.  It is then sent through glass fibers (strands).      We know, electric current flows through metal wire because electrons are pulled by voltage difference.  But how the light will travel through glass fibers without oozing out?  Imagine long narrow hall way.  Its walls fitted with mirrors.  Hallway goes zig-zag.  If you send a torch light beam to a mirrored wall, it will reflect and re-reflect on the walls again and again and travel trough the hallway.  Similarly, laser beam travels through glass strands using 'total internal reflections'.       Total internal reflection :  If a ray of light goes from glass to ai

CLASS V Student A :  What is the boiling point of water? Teacher:      100 degree c is said to be the boiling point of water. Student A:   Why 100 degree c ? Teacher:  At 100 degree c , water bubbles up and evaporates. Student A:  O.K. CLASS X Student B:  What is really happening at the boiling point? Teacher:  Liquid water changes into gaseous state.  At the boiling point, the water molecules gains enough energy to flight the air molecules and escapes into the atmosphere.  Hence at 100 degree c, the water vapour pressure and the atmospheric pressure equals. CLASS XII  Student C:  What you mean by 'liquid changes into gas'? Teacher:  The water molecules has positive end and the negative end.  The positive side of one molecule attracts negative side of another molecule.  Hence the water molecules cling together as a drop, as a liquid.  As the temperature increases, the molecules gains energy and break free from the electrostatic bonds.  The free molecules bubble

                A man should earn because everything has a price even drinking water.  A man starts earning after education.  His income will not be proportional to his work.  The earnings will be less than the quantum of his work  initially.  Because he is learning the trick and tools of the trade.  During the middle age of a man (Man includes woman), his income will match his work output.  When he further moves  into the old age, his income will increase but work and duty may decline.  Because, he mostly will do supervisory and management roles.      Incomes are two kinds.  One is active and the other is passive.  You earn active income by physically doing work, that is by doing day-job.  Passive income comes from rent, interest etc .  As you age, active income should decrease and passive income should rise. HOW TO RAISE THE PASSIVE INCOME?  1. By renting your property like house, shop, car etc.  Buying a new property and renting is not advisable or profitable.  Your inherit

1. Why the circular waves in the pond goes on expanding? 2. When you happened to be in a room, why all the outside noise appears to came from the door step? 3. Why tsunami affects only some parts of the land? 4. When any wave pass through a gap, it spread out in semi-circular fashion, why?      All these questions are answered by "Huygen's principle".  What is that?      Say, you drop a stone in a placid sheet of water.  Circular waves are created and starts expanding.  Huygen's principle says, "every point in a circular wave acts as a secondary source of waves.  And new wavelet starts from these points and move forward (as if a stone is dropped at every point of the circle).  The new wave front is the envelop (collection) of these wavelets".    This principle is a good tool (not a law) to predict the path and the progress of waves.  Now we can answer the above questions.: 1. Since every point on a wavefront act as source; the  new wavelets alwa

     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