By K.D. Pavate
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Extra resources for A Matter of Chance
It can be shown that for large values of n the binomial distribution reduces to a Poisson distribution. The example on AIDS can be simplified using the expression for Poisson distribution. Here in place of m we use p times the sample size which is 1000. 5 m=l/2 P(r) 0 1 2 3 r 4 1 m=l P(r) 0 1 2 3 4 5 m=2 P(r) 0 1 2 3 4 5 6 7 Poisson distribution — A well known probability model tabulated, so that the problem reduces to one of looking up the table. Poisson distribution has a curious history. About 150 years ago it came to the notice of the German army that one of the DISTRIBUTION OF CHANCE 55 causes of accidental deaths was on account of horses kicking the soldiers.
Suppose we had to elect two vice-presidents. Now, we are interested in which two members are elected and the order is of no consequence. For instance, announcing that PQ or QP have been elected makes no difference since both have been elected. So when two people have been elected without regard to their arrangement, then this "unordered" selection is called a "combinat i o n " . The m a t h e m a t i c i a n ' s w a y of e x p r e s s i n g this combination or unordered selection is: 50 A MATTER OF CHANCE "Cr = n!
When it comes to estimating P(M+W) we have to be a bit careful. If we were to add the number of sample points in event M and event W, we would have included the two sample points in the intersect twice over. In order to avoid this double counting we subtract the probability of the two points in the intersect. This leads us to the well known "addition" rule for two events M and W. The probability of the union of these two events is P(M+W) = P(M)+ P(W)P(MW). The numeric values are then inserted to find P(M+W).