# Probability: Basic concept, Definition, Questions and Solutions

Today I am going to discuss an important topic that is **Probability**. I hope you you would have solved all the homework questions easily but if you have not then you can always tell your doubts here at eckovation in the comment section. And for those who are reading my article for the first time here is the link http://banking.eckovation.com go and subscribe so that you get all the updates about competitive exams. So let us learn what is Probability.

**Basic Definition:-**

** **Probability has a very simple meaning that is extent to which something is likely to happen or be the case. Mathematically it means the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole numbers of cases possible.

**Basic Concept:-**

**Random Experiment:- **An experiment in which all possible outcomes are known and the exact output cannot be predicted in advance is called a random experiment.

**Sample space:- **When we perform an experiment then the set S of all possible outcomes is called the Sample space.

Eg- In tossing a coin, S = {H,T}

**Event:- **Any subset of a sample space is called an event.

**Solved Examples:-**

1. In a throw of a coin, find the probability of getting a head.

Solution: Here S = {H,T} and E = {H}.

P(E) = n(E)/n(S) = 1/2

2. Two unbiased coins are tossed. What is the probability of getting at most one head?

Solution: Here S = {HH, HT, TH, TT}

Let E = event of getting at most one head.

E = {TT, HT, HT, TH}

P(E) = n(E)/n(S) = 3/4

3. An unbiased die is tossed. Find the probability of getting a multiple of 3.

Solution: Here S = {1,2,3,4,5,6}

Let E be the event of getting a multiple of 3.

Then E = {3,6}

P(E) = n(E)/n(s) = 2/6 = 1/3.

4. In a simultaneous throw of a pair of dice, find the probability of getting a total more than 7.

Solution: Here, n(s) = (6 * 6) = 36

Let E = Event of getting a total more than 7

= {(2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2),(6,3), (6,4), (6,5), (6,6)}.

Therefore P(E) = n(E)/n(S) = 15/36 = 5/12.

**Homework Questions:- **

1. In a simultaneous throw of two coins, the probability of getting at least one head is

a. 1/2 b. 1/3 c. 2/3 d. 3/4

2. Three unbiased coins are tossed. What is the probability of getting at least 2 heads?

a. 1/4 b. 1/2 c. 1/3 d. 1/8

3. Three unbiased coins are tossed. What is the probability of getting at most two heads?

a. 3/4 b. 1/4 c. 3/8 d. 7/8

4. A basket contains 4 red, 5 green and 6 white balls. A ball is drawn at random from the basket, what is the probability that both are red? (S.B.I P.O. 2010)

a. 3/7 b. 1/2 c. 1/11 d. 1/6 e. none of these

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