# Properties of Probability

In mathematics, probability deals with the occurrence of a random event. It is used to predict how likely the events will happen. Probability has been used mainly in the fields of physical sciences, commerce, biological sciences, medical sciences, weather forecasting, etc. As far as the JEE exam is concerned, probability is an important topic. Students can easily score marks from this topic once they understand the topic clearly. In this article, we will learn the important properties of probability.

Bayes Theorem of Probability

Mutually Exclusive Events in Probability

Dependent Events

## 10 BasicProperties of Probability

1. The probability of an event E is defined as P(E) = [Number of favourable outcomes of E]/[ total number of possible outcomes of E].

2. The probability of a sure event or certain event is 1.

3. The probability of an impossible event is 0.

4. The probability of an event E is a number P(E) such that 0 ≤ P (E) ≤ 1. Probability is always a positive number.

5. If A and B are 2 events that are mutually exclusive, then P(A⋃B) = P(A) + P(B).

6. An elementary event is an event having only one outcome. The sum of the probabilities of such events of an experiment is 1.

7. The sum of probabilities of an event and its complementary event is 1. P(A) + P(A) = 1.

8. P(A⋃B) = P(A) + P(B) – P(A⋂B).

9. P(A⋂B) = P(A) + P(B) – P(A⋃B) .

10. If A1, A2, A3 ,………, An are mutually exclusive events, then P(A1 ⋃ A2 ⋃ A3… ⋃ An) = P(A1) + P(A2 ) + ………. + P(An)

## Solved Examples

Example 1:

Find the probability of getting an even number when a die is tossed.

Solution:

S = {1, 2, 3, 4, 5, 6}

Favourable events = { 2,4,6}

Number of favourable event = 3

Total number of outcomes = 6

Hence probability, P = 3/6 = ½

Example 2:

A carton consists of 200 watches of which 190 are good, 7 have minor defects and 3 have major defects. A merchant Reena will only accept the watches which are good, but another merchant Seema will only reject the watches which have major defects. One watch is drawn at random from the carton. What is the probability that it is acceptable to Reena? Also, find the probability that it is acceptable to Seema?

Solution:

A watch is drawn at random from 200 watches. So there are 200 equally likely outcomes.

No. of outcomes acceptable to Reena = 190/200 = 0.95

No. of outcomes acceptable to Seema = (190+7 )/200 = 197/200 = 0.985

Practice more Problems:

Probability Problems

JEE Past Year Questions Bank on Probability