sciencecapsules

           Virus is manometers sized particle.It is a RNA-genetic info. covered with protein and fat.  Structure of the corona virus has been found using powerful microscopes.  As you see, everywhere, it is a spherical shape with spikes.  Our sun's top layer is called corona sphere.  Light rays are seems to be coming out from corona sphere.  The virus' spikes looks like sun's corona-sphere.  Hence it is called corona virus.      It enters our body through eyes,nose and mouth; goes to the throat and lungs.  The spikes of the virus easily attaches with the cells in the lungs; it injects its RNA into the cell, multiplies itself many many times and finally destroys the host cell.  That is how, it damages the lung organ.  But the body's defense system (immune system) immediately swings into action.  Mostly,  our body's immune system (white cells, B-cells, T-cells) wins the battle.  But some times , virus hijacks and confuses the defense mechanism.  It even turns o

    In a class, there are 50 students.  80% of them are just average students.  But, remaining 20% is highly intelligent.  In a objective type examination, one student has scored very high marks.  Is he really intelligent?  Or an average student scored top marks out of sheer luck?  Let us find out.     The probability of intelligent students in the class is 80% or 0.80 -P(I).  The probability of the average students present in the class is 20% or 0.20 -P(A).  The probability of clever students winning-getting top marks is P(W/I) =0.60 (already known).  The chance for average students to win is P(W/A) =0.20 (already known).    The chance for winner being intelligent is got by applying Bayes theorem P(I/W) = P(clever/win) = P(A)*P(W/I)/(P(A)*p(W/I)+P(I)*p(W/A)) = 0.20*0.6/(0.2*0.6+0.8*0.2) =43%     43% is very less.  We cannot conclude that the winner is really smart.  Suppose, he scores well in the second test.  He may be smart.  The chance for smart boy to win second time

           US president's aide always carries a bridf case using which he can annihilate the world at any moment.  Yes, it is a black leather suitcase weighing 45 pounds and it is always within the reach of the US president.  It is nicknamed "nuclear foot ball".      On the day, the US president sworn in, he receives the world's most powerful ciphers(encrypted text) called the gold codes, they are printed on a plastic card similar to a credit card that is known as the BISCUIT.  They allow the president to identify him or herself as the authorized user of the foot ball.  President's carry the biscuit on their person day and night.    The nuclear football is carried by one of a series of rotating military aides who are always with the president, travelling in the same vehicle, taking the same elevator, and staying on the same floor of a hotel.  These aides have undergone extensive psychological testing.      The foot ball is a communications device for cont

           No one can lead a life without taking risk.  But, we have to calculate and minimize the risk.  We always think flying is riskier than travelling by car.  But, mathematically it is wrong.  There are about 4 fatalities in every million hours of flying -says planecrashinfo.com.  The corresponding figure for driving is 12 to 15 fatalities per billion miles.     There is a unit for measuring risk.  It is called "micromort" - invented by Stanford university professor Ronald A Howard.  "A micromort is a one -in - a -million chance of dying while undertaking an activity".     In England -2012, about 48 people died everyday from things other than natural causes, out of a population of 56.5 million - so  the probability of not surviving a day is 48/56500000 or 0.0000008.  We can also write, "the risk is 0.8 micromort".  In US, it is 1.6 micromort.     6 miles motor of bike ride carries a risk of 1  'micromort and so does a 250 mile drive in

         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%

        Matrix is square or rectangular table of numbers arranged in rows and columns.  It looks simple.  But its potential is immense.      If matrix is just another kind of numbers like integers, fractions, what is 0,1,-1 and i in matrix-kind.  We will find out.    First, we should learn matrix multiplication.          Multiplication of matrices is the important operation and it is highly useful.  To multiply two matrices, number of rows of one matrix must be equal to the number columns of another matrix. MULTIPLYING MATRIX A AND B [a b  * [e f   = [ae +bg  af +bh  c d]     g h]     ce +dg   cf +dh]   A         B     =           C This is how you multiply order of two matrices.      Column elements in one matrix is multiplied by corresponding row elements in another matrix and summed up to get the new element. Why we multiply this way? Consider this set of equations. 4x +2y+z  = 10 2x +3y+4z =25 [4 2 1  * [x  = [10  2 3 4]     y      25]                z]  

         We are enchanted by red sunset, Blue-sky, white water falls, green tea estate.  What is color actually?  We know, light is origin of color.  We also know light is electromagnetic wave.  The wave's characteristics are wavelength and frequency.  Each color is electromagnetic wave with certain range of frequency.  For example, blue light has frequency range-610-670 T Hz.      The sun burns and emits light.  It emits characteristic seven colors as indicated by rainbow.  Sodium burns in sodium lamp and emits yellow light.  Neon gives out blue light.  Argon-red.  Each element gives out its own signature color or colors called spectrum.      White light is a mixture of colors.  It split into constituent colors when sent through prism.  We also get Rainbow due to prismatic effect of raindrops.  Some times, when light waves meet, some colors are destroyed and some other colors are reinforced (interference of light).  This is what happens in soap bubble, oil film on wet sur

          You are running a grocery store.  From experience, you know 4.6 customers arrive per hour.  You want to serve all of them almost without wait (90%).  How many salespersons you require?      In statistics, there is topic called 'Poisson distribution'.  A formula in that topic tells us that the probability of number of customers arriving in an hour.      4.6-N - No. of customers arriving per hour.      P(K) = e ^-N * N^K/K!      P(K) - probability of K customers arriving per hour,      K!  - Factorial K - K*(K-1)*(K-2) ... 1      e - 2.71 ....Euler's constant.      The chance of '0'customer to show up      = e^-4.6 * 4.6 ^0/0!      =e^-4.6 *1/1      =2.71 ^-4.6 = 0.010    Probability of '1' customer =e^-4.6*4.6^1/1!                             = 0.046 for 2 customers   = 0.106 for 3 customers  = 0.163 for 4                     = 0.188 for 5                     = 0.173 for 6                     =0.132 for 7                   

The statisticians used to tell these jokes. 1. We humans have 1.999... legs on the average.  It will happen when we take into account physically challenged people. 2. We have only one testicle. Again this will result when all women are taken into account. 3. In a survey, men were asked how many girl friends they have.  Most of them reported one.  But a few reported 5 to 10.  Some even 100.  If we take a simple average, the answer will be shocking and misleading.     We have to use not only average -mean, but also mode and median at the appropriate places.  Let us explore. MEAN:  The average we use every day.  It is got by adding all the items and dividing by no. of items.  It is suitable for the data which cluster around a central value.  Example:  Height of male or female graduate students.  Blood pressure values of persons in the age range 60-70. MEDIAN:  It is the number that lies in the middle when all the numbers in the data sheet are lined up in ascending order.Say, t

         In India, nearly 17 people per 100000 meet with fatal accident every year( Wikipedia).  What is one's chance of survival here?     17 in 100000 can be written as 0.00017 - the probability falling victim to an accident.  The probability of 'not falling victim' is 1-0.00017= 0.99983.  Again what is your chance of 'not meeting with accident' in your life-time.  (say 70 years) = (0.99983)^70 = .9882 What is the chance of falling victim in your life time?(Again reverse the probability) That is 1-0.9882 = 0.0118 =1/85. The chance is 1 in 85 for meeting a fatal accident in one's life span in India.     In UAE, there are only 4.4 victims per 100000.  If you work out the same calculation, the chance of getting into accident will be very  less there.      In the city of Sanpedrosula in Honduras about 160 people per 100000 fall victim to homicide.  If you work out in the same way, the chance is 1 in 9. If this remained constant over a time, one ma

        We know "the" is the most occurring word in English language. I want to find out how many 'the' occurs in a sentence normally.  In a passage of 100 words, mostly 7 'the' occurs.  The probability of occurrence is 0.07.  Also, it is found that normally English sentence contains 19 words.      The probability of occurrence of two 'the' in a sentence of 19 words is, = C(19,2)* 0.07^2 * 0.93 ^17 = 24.4% Let us understand the formula step by step. 1. The probability of 'the' not being present is 1-0.07 =0.93.  The probability of 'the' not being one of the 17 words is 0.93^17. 2. The chance of 'the' appearing two times is 0.07^2. 3. C(19,2) is called combination or binomial co-efficient.  It gives, the no.of ways two 'the' and the remaining 17 words can be arranged.  Refer foot-note.  All the three factors should be multiplied to get the correct probability.  It gives 0.244 or 24.4%.      Similarly wha

         Can a monkey type out a meaningful sentence.  Let us explore using statistics.      First, let us learn "multiplication rule".  What is the chance of getting three heads consecutively (coin toss).  We know, probability of getting a head is 1/2.  The 'three coin throws" are independent events.  That is, one out come in a throw does not influence the next throw.  In this case, we can use multiplication rule.  The total probability is obtained by multiplying the individual probabilities.  Hence the chance of getting 3 heads in a row is 1/2*1/2*1/2 = (1/2)^3 = 1/8.  If you do 'the three tosses' eight times, one set may be successful and yield three heads.  Hence multiplication plays vital role in statistics.     Now Shakespeare's Romeo and Juliet. "Two households, both alike in dignity In fair Verona, where we lay our scene" .  It has 77 letters.      We know a monkey can type randomly.  By any chance, can it type the above two se

           A is proportional B.  C is inversely proportional to square of D.  This kind of laws are common in physics.  If one quantity depends on another, there must be some number bridge connecting both . That is; A "is proportional to" B      How to make to A "is equal to" B     Here we put a "constant" K , A fixed value, a unchanging number between them.     A= K *B If we find K, the problem is solved.  We get a accurate relationship between A and B.     One way to get K is; K = A/B Make number of trials (experiments), find A  and B for each trial; divide them and get the average value of K.  The "K" will be mostly correct, if the law holds good. Another way, if B is equal one, then K will be equal to A.  Third way, you can find K using trial and error method.  That is 'guessing'.   Let us go for some examples . Draw a circle.  Let it grow.  As the circumference C grows, its diameter 2 r  also grows.  Let r be its

           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