In all probability …
Probability (or Px as mathematicians call it) is a much heard of but little understood mathematical concept. People often say..there is a good chance that this train ticket will get confirmed… or in all likelihood that Congress will get a majority in Karnataka . Now when you start putting a number on “good chance” or “all likelihood” , you have Px. So u can say there is a 70 percent chance that the ticket will get confirmed or there is a 80 percent chance that Congress will get majority (fat chance !!)
In more serious mathematics , Px is expressed as a number between 0 and 1. So if the likelihood of an event NOT happening is ZERO, we say Px= 0 and if it is certain to happen then we say Px= 1. Now here is where maths departs from day to day experience. What maths says is that there is NO event yet to happen where Px= 1. So for anything that has NOT YET happened , there is ALWAYS a chance, however small that it will not happen.
How about the event “The sun will rise tomorrow” ? Is it not certain to happen? Well , mathematicians say , yes it is MOST likely to happen, but NOT CERTAIN to happen. Px is very close to 1 (say 0.9999999999 and on) but less than 1. Here is how to understand this
· Let us say the earth has a life of 6 billion years. On the last day of earths life , there will be no sunrise on the next day (there will in fact be no next day).
· There is also a possibility that the Earth may be completely blown up and cease to exist even tonight as a result of some unknown cosmic catastrophe.
But cosmic events are not the only things that involve Px. Everyday life has many examples. Casino’s use it extensively. It’s also used in the design (how many) of service counters to provide at a railway station, or in a supermarket or in deciding insurance premiums. Here is a very interesting example.
When a borewell is drilled for water, it sometimes ends up dry. So the money is literally down the drain. Now with this risk how can farmers dig wells in rural areas ? Insurance companies step in. From previous data on wells in a particular area, they estimate the probability of a dry well (say 5 out of every 100). Then they calculate a premium. So now the farmer can pay a small amount to overcome the risk. If the well is dry, the insurance company re-imburses expense to the farmer. If the well is not dry, the company keeps the insurance premium. Over hundreds of drillings they make a profit and the farmers’ risk is taken care of . Medical , accident and auto insurance all work on the same principle.
Probability (or Px as mathematicians call it) is a much heard of but little understood mathematical concept. People often say..there is a good chance that this train ticket will get confirmed… or in all likelihood that Congress will get a majority in Karnataka . Now when you start putting a number on “good chance” or “all likelihood” , you have Px. So u can say there is a 70 percent chance that the ticket will get confirmed or there is a 80 percent chance that Congress will get majority (fat chance !!)
In more serious mathematics , Px is expressed as a number between 0 and 1. So if the likelihood of an event NOT happening is ZERO, we say Px= 0 and if it is certain to happen then we say Px= 1. Now here is where maths departs from day to day experience. What maths says is that there is NO event yet to happen where Px= 1. So for anything that has NOT YET happened , there is ALWAYS a chance, however small that it will not happen.
How about the event “The sun will rise tomorrow” ? Is it not certain to happen? Well , mathematicians say , yes it is MOST likely to happen, but NOT CERTAIN to happen. Px is very close to 1 (say 0.9999999999 and on) but less than 1. Here is how to understand this
· Let us say the earth has a life of 6 billion years. On the last day of earths life , there will be no sunrise on the next day (there will in fact be no next day).
· There is also a possibility that the Earth may be completely blown up and cease to exist even tonight as a result of some unknown cosmic catastrophe.
But cosmic events are not the only things that involve Px. Everyday life has many examples. Casino’s use it extensively. It’s also used in the design (how many) of service counters to provide at a railway station, or in a supermarket or in deciding insurance premiums. Here is a very interesting example.
When a borewell is drilled for water, it sometimes ends up dry. So the money is literally down the drain. Now with this risk how can farmers dig wells in rural areas ? Insurance companies step in. From previous data on wells in a particular area, they estimate the probability of a dry well (say 5 out of every 100). Then they calculate a premium. So now the farmer can pay a small amount to overcome the risk. If the well is dry, the insurance company re-imburses expense to the farmer. If the well is not dry, the company keeps the insurance premium. Over hundreds of drillings they make a profit and the farmers’ risk is taken care of . Medical , accident and auto insurance all work on the same principle.
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