Probability is the bane of the age,' said Moreland, now warming up. 'Every Tom, Dick, & Harry thinks he knows meaning of probable. The fact is most of the people have not the smallest idea what is going on round them. Their conclusions about life are depends on utterly irrelevant - and usually inaccurate - premises.
The probability of 7 when rolling 2 die is 1/6 (= 6/36) because the sample space includes of 36 equiprobable elementary outcomes of which 6 are favorable to the event of getting 7 as the sum of 2 die. Denote this event A: P (A) = 1/6.
Let us take another event B which is having at least one 2. There are 36 elementary outcomes of which 11 are favorable to B & therefore, P (B) = 11/36. We do not know whether B happens or not, but this is a legitimate question to inquire as to what happens if it does. More particularly, what happens to the probability of A under the assumption that B took place?
The hypothesis that “B” took place reduces the set of possible outcomes to 11. Of these, only 2 – 25& 52 - are favorable to “A”. Since this is logical to assume that the 11 elementary outcomes are equiprobable, the probability of “A” under the assumption that B took place equals 2/11. This probability is denoted P (A|B) - the probability of an assuming B: P (A|B) = 2/11. More explicitly P (A|B) is said to be as conditional probability of an assuming B. Of course, for any event A, P (A) = P (A|Ω), where, by convention, Ω is the universal event - the whole of the sample space - for which all available elementary outcomes are favorable.
In our next blog we shall learn about conditional probability distribution I hope the above explanation was useful.Keep reading and leave your comments.
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