PROBABILITY

PROBABILITY

POINTS TO REMEMBER

1.   A random experiment is an experiment in which;

(i)           All the outcomes of the experiment are known in advance, and

(ii)          The exact outcome of any specific performance of the experiment  is unpredictable, i.e. not known in advance.

2.   The set of all possible outcomes of a random experiment is known as a sample space associated with the random experiment.

3.   An event is something that happens

4.   Ordinarily speaking, the probability of an event denotes the likelihood of its happening.

5.   Definition of probability of an event: If there are n events associated

with a random experiment and m of theme are favorable to an event A, then the probability of happening of A is denoted  by P(A) and is defined as the ratio m / n

Thus, P(A) =    Number of favorable outcomes

                       Total number of possible outcomes

              i.e., P(A) = m/n

6.      Clearly, 0 ≤ m ≤ n Þ 0 ≤  m ≤ 1 Þ 0 ≤ P(A) ≤ 1.

                                                n

          All probabilities must have a value greater than or equal to 0 and less than or equal to 1.

6.      Since the number of cases in which the event A will not happen is    n – m, therefore if A denotes non-happening of event A then the probability P(A) of non-happening of event A is given by

 P(A) = n – m  = 1 – m = 1- P(A)

               n                n

Þ P(A) + P(A) = 1

i.e., if p is the probability of an event happening, then the probability of the event not happening must be 1 – p, in the case of mutually exclusive events.

8.      An event which is certain (sure) to happen has a probability of 1 (or  100%).

          For example, the probability that the sun will rise in the east is 1.

9      An event which is impossible has a probability of 0 (or 0%)

          For example, the probability that the sun will never set again is 0.