By K.D. Pavate
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5 x 4 x 3 x 2 x 1 ) / ( 3 x 2 x l ) = 5 x 4 = 20. This is exactly the number we obtained by organizing the matrix above. Only we based our earlier estimate on commonsense. In the matrix also, the first letter stands for the president and the second for the vice-president. The two positions are different in hierarchy Consequently, the order in which the two persons have been elected is important. 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.
A time honoured way of measuring an individual or subjective probability is to "lay a bet". We have considered three alternative ways of defining probability and in the process explained how measures of probability are arrived at. The first way was to examine the situation or the problem theoretically and then to estimate its probability of success. One usually makes use of the principle of equal likelihood to the outcomes of such random experiments. A word of caution is that not all outcomes are equally likely to happen.
On the other hand, when we compute P(B/A) we ask ourselves how probable it is that we are in B knowing that we must also be in A. The sample space shrinks from S to A. Thus, there are two ways of computing the conditional probability P(B/A). The first method is by considering the probability of B with respect to the reduced sample space A. The other method is to first calculate or estimate P(AB) and P(A) with respect to the original sample space S and subsequently take their ratios. This concept of conditional probability can be used to evaluate the probability of the simultaneous occurrence of two events: P(AB) = P(B/A)P(A) We can extend this idea to compute the probability of a single event A.
A Matter of Chance by K.D. Pavate