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Probability is a numerical possibility of some event. It is a chance of occurrence of a particular event out of all possible events.

Sample Space: Sample space is a set of all possible outcomes that are possible. In mathematics, it is denoted by n(S)

Event: No of ways in which the particular event can occur. It is denoted by symbol n(E)

Probability: It is denoted by symbol P(E)

Formula: P(E) = n(E) / n(S)

Examples: 10 balls labeled through 1-10 are placed inside a box. A random ball is taken out. What is the probability that the ball has a label greater than 2?

Solution:

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; n(S) = 10

E = {3, 4, 5, 6, 7, 8, 9, 10}; n(E) = 8

P(E) = n(E)/n(S) = 8/10 = 4/5

Given below are top 5 MCQs on probability:

A box contains 5 Green and 3 Red balls. A random ball is taken out. What is the probailiby that ball is red?

1. 1/7
2. 3/8
3. 2/4
4. 5/8

Solution: n(S) = 8; n(E) = 3

P(E) = n(E)/n(S) = 3/8

13 clothes marked from 1-13 are placed inside a case. A random piece of cloth is taken out. What is probability that the selected piece has mark greater than 4:

1. 2/3
2. 4/13
3. 9/13
4. 8/26

Two boxes (One Black and one Red) contain 5 balls each. The balls are labeled from 1-5. One ball from each box is taken out. What is the probability that the sum of labels is greater than 8:

1. 1/8
2. 5/8
3. 3/25
4. 5/25

Solution:

The sample-set for the given case is:

(1,1) (1,2) (1,3) (1,4) (1,5)
(2,1) (2,2) (2,3) (2,4) (2,5)
(3,1) (3,2) (3,3) (3,4) (3,5)
(4,1) (4,2) (4,3) (4,4) (4,5)
(5,1) (5,2) (5,3) (5,4) (5,5)

n(S) = 25

Summing numbers:

2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
5 6 7 8 9
6 7 8 9 10

In our set we have 3 elements that satisfy given condition. So

n(E) = 3

P = n(E)/n(S) = 3/25

A box contains 5 Green and 6 Red balls. A random ball is taken out. What is the probailiby that ball is red:

1. 4/9
2. 1/2
3. 5/11
4. 6/11