Question

3a.What does the probability of an event E say, and how is it denoted symbolically?

3b. Are there any limitations to the measured value of the probability of an event?

Answer 1

SOLUTION:

3a.

Probability of an event E is defined as the number of outcomes favourable to E divided by the total number of equally likely outcomes in the sample space S of the experiment.

Symbolically, probability of event E is written as P(E).

So for instance, if we consider rolling of a fair die as an experiment, the sample space S contains all possible outcomes i.e. {1, 2, 3, 4, 5, 6}, all of which are equally likely. Now if we consider an event E as getting an even number, the outcomes favouring E are {2, 4, 6}.

Thus, probability of getting an even number on rolling a fair die is:

3b.

Yes, there are limitations to the measured value of the probability of an event. The probability of an event E (say) lies in the interval [0,1]

If P(E) = 0, it is called an impossible event.

If P(E) = 1, it is called a sure event.