Table of contents  
Definition of Probability  
Probability line  
Random Experiment  
Mutually Exclusive Events  
Equally Likely Events  
Independent Events  
Compound Events  
Probability Formulas 
Probability always lies between 0 to 1. If your answer exceeds 1 then your answer is incorrect.
Experiment: In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a welldefined set of possible outcomes
Outcome: In probability theory, an outcome is a possible result of an experiment. Each possible outcome of a particular experiment is unique
Sample Space: The welldefined set of possible outcomes is known as the sample space.
A random experiment is an experiment or a process for which the outcome cannot be predicted with certainty.
Example:  Drawing 2 cards from a well shuffled pack is a random experiment while getting an Ace & a King are events.
In probability theory, two events) are mutually exclusive if they cannot both be true or occur at the same time.
Example: The events of getting a head or a tail when a coin is tossed are mutually exclusive.
Equally likely events are events that have the same theoretical probability (or likelihood) of occurring.
Example: When a die is thrown, any number from 1 to 6 may turn up. In this trial, the six events are equally likely.
Two events E1 and E2 are said to be independent, if the occurrence of the event E 2 is not affected by the occurrence or the nonoccurrence of the event E1.
To find the probability of two independent events that occur in sequence, find the probability of each event occurring separately, and then multiply the probabilities. This multiplication rule is defined symbolically below. Note that multiplication is represented by AND.
Multiplication Rule 1: When two events, A and B, are independent, the probability of both occurring is:
P(A and B) = P(A) · P(B)
When two or more events are in relation with each other, they are known as compound events.
Example:  When a die is thrown and a coin is flipped the occurring events are called compound events.
Example 1: Find the probability of getting a head in a throw of a coin.
Sol: When a coin is tossed we either get head or tail upwards.
So, total number of cases= 2 = n,
number of favorable cases to get H = 1 = m
P (H) = No. of favorable cases/ Total no. of outcomes = (m/n)
=1/2
Example 2: An unbiased die is rolled. Find the probability of a) Getting a multiple of 3 b) getting a prime number
Sol:
When a die is rolled we can get any one of the numbers from 1 to 6.
Total number of cases = n = 6
(a) Let event A= getting a multiple of 3
Then A= {3.6}.
Therefore m=2
P (A) = m/n = 2/6 = 1/3
(b) Let event B = getting a prime number
Then B= {2, 3, 5}.
so, m = 3
P (A) =m/n=3/6=1/2
Example 3: A card is drawn from a wellshuffled pack of 52 cards. Find the probability that
(a) Card drawn is red
(b) Card drawn is Queen
(c) Card drawn is black & king
(d) Card drawn is red & number card
(e) Card drawn is either king or queen
Sol:
Before solving this problem, let us recall the game of cards. One deck of cards contains totally 52 cards. Among them we have 13 spades & 13 clubs which are black in color, 13 diamonds & 13 hearts all of which are red. In the 13 spades, 9 are numbered cards, numbered from 2 to 10, one ace card & 3 face cards namely J, Q & K. Similarly for the clubs, diamonds & hearts also.
Totally there are 52 cards & any one can be drawn
So, total number of cases = n = 52
(a) There are 13 diamonds & 13 hearts which are red
Number of red cards = m = 26
P (getting red) =26/52=1/2
(b) There are 4 queens = 4
P (getting queen) = m/n=4/52
=1/13
(c) The king of spade & clubs are black
No. of cards which is king & black=m=2
P (king & black) =m/n =2/56
=1/26
(d) The 9 number cards of hearts & 9 number cards of diamonds are red.
No. of cards which are red & number cards = m = 18
P (red & number)=m/n=18/52
=9/26
(e) There are 4 queens & kings
No. of favorable case = m = 8
P (queen or king) = m/n = 8/52
= 2/13
Example 4: A bag contains 6 white beads & 4 red beads. A bead is drawn at random. What is the probability that the bead drawn is white?
Sol: Total no. of beads in the bag = 6+4 =10. n= 10
Any one of the 6 white beads can be selected, m=6
Therefore, P (getting white bead) = m/n=6/10
=3/5
Example 5: A box contains 8 red marbles, 6 green marbles & 10 pink marbles. One marble is drawn at random from box. What is the probability that the marble drawn is either red or green?
Sol: Total number of marbles= 8+6+10 =24, n=24
There are 6 green & 8 red marbles
Therefore, number of favorable cases=6+8=14
P (red or green) = 14/24=7/12
Here are some basic probability formulas that are frequently used in quantitative aptitude exams, along with a table for quick reference:
Note: P(A) represents the probability of event A. P(BA) represents the probability of event B given that event A has occurred. P(A and B) represents the probability of both events A and B occurring.
1. What is the definition of probability? 
2. What is a random experiment? 
3. What are mutually exclusive events? 
4. What are equally likely events? 
5. What are independent events? 

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