When I first learnt about Probability Theory in secondary school, I went nuts! I fell in love with it, as it seemed almost magical that we could somehow synthesize or calculate the probability of something happening! I feel like I’m a psychic! Boy, was it fun finding out that the chance of a ‘1’ occurring from an unbiased dice was 1/6 or 0.1666666… 6667… or that the chance of even numbers occurring was 1/6 + 1/6 + 1/6 or 3/6 or 1/2. Ok, it is intuitive to arrive at 0.5 or half, but the maths behind it is the marvel.
The other thing that was fun about probability was that there were the card games. It seem like many math teachers are very into card games as many questions revolves around the probability “of drawing the next Ace from the deck, given a certain hand that was already played”. I half guess that this obsession with cards might have stem from the poor financial status of teachers in general. Literature and linguistic teachers will poke fun at the social rich strata while the mathematicians will dream about striking it rich by winning at this weekend’s poker game or blackjack! Of course, there are the boring apple and oranges in a bag questions and red and blue marbles questions, but those are for kids and no one got rich guessing apples and oranges or marbles!
We learn from Mathematics, more rightly Statistics or Probability Theory, that for an event A that has N unbiased outcomes O, the probability of O1 occurring is 1/N or 100/N%.
Further, if an event A exist whose outcome Oa is dependent on both event B & C occurring, then probability of Oa = Ob X Oc. If for an event Am whose outcome Oam depends on M events, then Oam = O1 X O2 X O3 X … … X Om-1 X Om.
Probability of event A whose outcome Oa is dependent on either event B or C occurring, is (Ob + Oc)/2. Similarly for M events, Oam = (O1 + O2 + … + Om-1 + Om) /m. P(B OR C) = Pb + Pc – P(B AND C).
For M events, P(O1 or O2 or … or Om) = P(O1) + P(O2) + … … + P(Om) – P(O1 and O2 and … … Om).
… where Events B, C, O1 to Om are independent events.
We also know that an impossible event has outcome Oi with probability of 0 (ZERO) (eg, the sun rising from the west tomorrow) while an event that will happen has outcome Ow with probability of 1 (ONE).
So consider an alternate world where people were incessantly happy. Constantly bursting with joy, it would take … no, it would be an impossibility to be unhappy. And there is no different grades of happiness or joy. In fact, they only have one word to describe it,
and it is called Joy; it is only our imperfect world with lousy cultural trappings that we even attempt to wonder if that is possible.
Everything is well in this world and then one day, someone A decided to ask person B to do action C with outcome Oc. Under normal circumstances, everything would have gone accordingly and we would have to find another story to tell. But fortunately for us, person B decided not to do action C; instead he did action D with outcome Od. The chance or probability of this to happen is (1 – Pc) or Pc’ (the chance of C not happening). What’s most interesting was that when C did not happen, A became upset! So the event “A become upset” had the probability of Pc’ or 1 – Pc, and probability of A’s happiness is suddenly no longer 1 (a definite eventuality) but 1 – Pc’ or Pc. So when A decided to hinge his happiness to event C, his happiness became Pc and not 1. This is not a problem if Pc = 1, but since there is a chance for C not to happen (it depends on person B), then Pc is distinctively less than 1.
When news of an unhappy person being in existence, fear spread quickly. The chance of unhappiness was zero and now fear even creep in! A council was formed to remove this unhappy probability. While the important council people were having their meetings, person A started pondering why B did not do C but D instead. He tried asking B for an explanation but got rejected leading to further unhappiness! Now, A not only need C to happen, he also need explaination E to happen … he went on to ask person B1, B2 … to Bn for an answer, but the probability of them all giving an answer were P1, P2 … and Pn respectively. So now the probability of A being happy was Pc X Pb X P1 X P2 X … X Pn.
With each person he added onto the list, the probability of his happiness shrunk. And besides him, many others started pegging their happiness people’s actions, to events and to things. They started thinking “If only I can have that … … I will be happy!”, “If only she will do that for me … … I will be happy!”, “If only he will … … I will be happy!” … … and over time, people’s happiness hinged on one too many things, and people were mostly unhappy. And what happened to the council of important people you ask? They too got upset because they thought “If only they would agree with me, then I would be happy!” … …
If you think this is a funny story about a mathematically impossible world, think again. Aren’t we the ones who put a condition to our own happiness, thereby reducing our probability of being happy?
If we look at our life and consider the times when we were happy or not, we would find that most of our happiness depends on conditions. It depends on people, their actions or inaction, on things and many more. It depends on many. When we are young, our happiness are simpler. We may need just a pencil and paper to doodle, and we can be content and happy. As we grow up, we start to pursue more and more to satisfy ourselves. We start to need more to be happy. But is that truly happiness? Or is that the sure way to an impossible or at best fragile happiness?
Think again. Do your math.