PROBABILITY

It is remarkable that a science, which began with the consideration of

games of chance, should be elevated to the rank of the most important

subject of human knowledge.

—Pierre Simon Laplace

1.

An event for an experiment is the collection of some outcomes of the experiment.

2.

P(E) =

Total number of trials

3.

Example 9 :

Chapter 14), which gives the weights of 38 students of a class.

(i) Find the probability that the weight of a student in the class lies in the interval 46-50 kg.

(ii) Give two events in this context, one having probability 0 and the other having probability 1.

Consider the frequency distribution table (Table 14.3, Example 4,

Solution :

weight in the interval 46 - 50 kg is 3.

So, P(weight of a interval 46 - 50 kg) = 

(i) The total number of students is 38, and the number of students with3   = 0.079

                                                  38

  38 = 1.

Example 10 :

were kept under standardised conditions favourable to germination. After 20 days, the

number of seeds which had germinated in each collection were counted and recorded

as follows:

Fifty seeds were selected at random from each of 5 bags of seeds, and

Table 15.11

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Bag	1	2	3	4	5
Number of seeds germinated	40	48	42	39	41

What is the probability of germination of

(i) more than 40 seeds in a bag?

(ii) 49 seeds in a bag?

(iii) more that 35 seeds in a bag?

Solution :

(i) Number of bags in which more than 40 seeds germinated out of 50 seeds is 3.

P(germination of seeds in a bag) = 3= 0.6

                                               5

Total number of bags is 5.

(ii) Number of bags in which 49 seeds germinated = 0.0 = 0.5 = 1.                                      5 In all the examples above, you would have noted that the probability of an

Remark :

event can be any fraction from 0 to 1.

P(germination of 49 seeds ) =

                                        5

(iii) Number of bags in which more than 35 seeds germinated = 5.

So, the required probability =

(ii) For instance, consider the event that a student weighs 30 kg. Since no student has

this weight, the probability of occurrence of this event is 0. Similarly, the probability

of a student weighing more than 30 kg is

                                                                  38

The Probability of an event lies between 0 and 1 (0 and 1 inclusive).The empirical (or experimental) probability P(E) of an event E is given byNumber of trials in which E has happened