Here is your essay on probability of the occurrence of the desired event !
Probability is a measure of the relative chance of the occurrence of an event from among a set of alternatives. If there are N equally likely ways in which an event can happen and if n is the number of ways in which the desired can occur, then the probability of the occurrence of the desired event is given by n/N and is generally denoted by p. Since p is a measure of the relative chance to the totality of equally likely events, its value does not exceed 1. All the values of p lie between 0 and 1, both limits inclusive.
The rolling of an ordinary, cubical die may result in any one of the six different faces facing upward. The group of six possible results is said to be exhaustive. The possibility of die standing on its edge is not considered! The six possible results are said to be mutually exclusive since the occurrence of one result precludes the happening of the other. The rolling of the die is called a trial.
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Suppose that the die is a perfect cube made of homogeneous material and that there is no reason to expect that any particular face will come upper most frequently than any other. The six possible results are said to be equally likely, or equally probable.
If a trial may result in any one of n exhaustive, mutually exclusive and equally likely outcomes and if m of these outcomes entail the occurrence of an event E, then the probabilities that E will happen as the result of the trial is given by P(E) = p = m/n.
Since 0 ≤ m ≤ n, p is a positive number less than, or equal to unity. Since the number of outcomes involving the failure of E is n – m, the probability of the failure of E, denoted E, is given by
p (E) = q = (n – m)/n = 1 — m / n = 1 — p
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Further, p + q = 1
Example:
Sex determination in bisexual organism is a chance event. For a normal fertilization of an ovum, there are only two equally likely ways. The zygote may develop into a male or female depending on the type of gamete the male parent provided in animals (man, Drosophila, etc.) but in poultry it depends on the type of gamete the egg contains because in poultry female is the heterogametic sex.
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The gamete produced by the heterogametic sex may or may not contain the X-chromosome and these are equally likely too. So the chance that a fertilized egg will develop into particular sex is 1/2.
