I was tired and sleepy after my 4 mile walk..
Sasa asked me to answer a question:
The max number of hair on human head = 2 lakh
population of a city is 40 lakh
what is the probability that 2 ppl will have same number of hair..
I did come up to the answer = 1, but not with the speed and alacrity that Sasa expected.
Sasa claimed the answer was so obvious that I shouldnt have taken even a tired longer moment. Sasa calls it pigeonhole axiom. Say there are 4 pigeonholes and 5 pigeons, what is the probability that at least 1 pigeonhole will have >1 pigeon? Ans = 1. (Typical Dee quip: how do you know that every pigeon wants to go in the hole and n ot spread its wings a bit? )
I ranted that Sasa will make me prove all the axioms next, like prove that multiplication of 2 negative nos is positive. Bad example for a rant. Sasa really made me prove it!
Here goes my proof..
Proove that multiplication of 2 -ve integers is +ve. If I can prove this, extend the logic to all -ve numbers.
Lets see how 2*3 works..
multiplication is defined as repetitive addition.. 2*3 = 2 + 2 + 2
so a* 3 = 0 + a + a + a
so a* (-3) = 0 -a -a -a
so, -2 * -3 = 0 - (-2) - (-2) - (-2) = +6
hence -2 * -3 = +ve
hence proved that multiplication of 2 -ve integers is +ve.
I joked that if this was a 10th standard board exam question, this proof would have been wrong, as in would not have earned me any marks. :P
Sasa asked me to answer a question:
The max number of hair on human head = 2 lakh
population of a city is 40 lakh
what is the probability that 2 ppl will have same number of hair..
I did come up to the answer = 1, but not with the speed and alacrity that Sasa expected.
Sasa claimed the answer was so obvious that I shouldnt have taken even a tired longer moment. Sasa calls it pigeonhole axiom. Say there are 4 pigeonholes and 5 pigeons, what is the probability that at least 1 pigeonhole will have >1 pigeon? Ans = 1. (Typical Dee quip: how do you know that every pigeon wants to go in the hole and n ot spread its wings a bit? )
I ranted that Sasa will make me prove all the axioms next, like prove that multiplication of 2 negative nos is positive. Bad example for a rant. Sasa really made me prove it!
Here goes my proof..
Proove that multiplication of 2 -ve integers is +ve. If I can prove this, extend the logic to all -ve numbers.
Lets see how 2*3 works..
multiplication is defined as repetitive addition.. 2*3 = 2 + 2 + 2
so a* 3 = 0 + a + a + a
so a* (-3) = 0 -a -a -a
so, -2 * -3 = 0 - (-2) - (-2) - (-2) = +6
hence -2 * -3 = +ve
hence proved that multiplication of 2 -ve integers is +ve.
I joked that if this was a 10th standard board exam question, this proof would have been wrong, as in would not have earned me any marks. :P
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