Probability And Statistics

Probability And Statistics: Let us learn the importance of these two concepts in math. Probability is all about chance. Whereas statistics is more about how we handle various data using different techniques.  It helps to represent complicated data in a very easy and understandable way. Statistics and probability are the most important topics which are introduced in Class 10, Class 11 and Class 12 students are preparing for school exams and competitive examinations. The introduction of these fundamentals is briefly given in your academic books and notes.

Probability And Statistics

List of Probability Topics

Basic probability topics are:

Addition Rule of Probability Binomial Probability Bayes Theorem
Compound Events Compound Probability Complementary Events
Conditional Probability Complementary Events Coin Toss Probability
Dependent Events Experimental Probability Geometric Probability
Independent Events Multiplication Rule of Probability Mutually Exclusive Events
Properties of Probability Probability Line Probability without Replacement
Random Variables Simple Event Sample Space
Tree Diagram Theoretical Probability Types of Events

List of Statistical Topics

Basic Statistics topics are:

Box and Whisker Plots

Comparing Two Means Comparing Two Proportions
Categorical Data Central Tendency Correlation
Data Handling Degree of freedom Empirical Rule
Frequency Table Five Number Summary Graphical Representation of Data
Histogram Mean Median
Mode Data Range Relative Frequency
Population and Sample Scatter Plots Standard Deviation
Ungrouped Data Variance

Probability and Statistics Formulas

Probability Formulas: For two events A and B:

Probability Range Probability of an event lies between 0 and 1 i.e. 0 ≤ P(A) ≤ 1
Rule of Complementary Events P(A’) + P(A) = 1
Rule of Addition P(A∪B) = P(A) + P(B) – P(A∩B)
Mutually Exclusive Events P(A∪B) = P(A) + P(B)
Independent Events P(A∩B) = P(A)P(B)
Disjoint Events P(A∩B) = 0
Conditional Probability P(A|B) = P(A∩B)/P(B)
Bayes Formula P(A|B) = P(B|A) P(A)/P(B)

Statistics Formulas : Some important formulas are listed below:

Let x be item given and n is the total number of items.

Mean (Sum of all the terms)/(Total number of terms) = \(\overline{x}=\frac{\sum x}{n}\)
Median M = \((\frac{n+1}{2})^{th}\) : If n = odd

M = \(\frac{(\frac{n}{2})^{th}term+(\frac{n}{2}+1)^{th}term}{2}\) : If n = even

Mode   Most frequently occurring value
Standard Deviation SD (σ) = sqrt[Σ( x_i – μ )x^2/N ]
Variance Var(x)  = E[(x – μ)^2] = E[x^2] – μ^2

Solved Examples:

Example 1: Find the mean and mode of the following data: 2, 3, 5, 6, 10, 6, 12, 6, 3, 4.

Solution:

Total Count: 10

Sum of all the numbers: 2+3+5+6+10+6+12+6+3+7=60

Mean = (sum of all the numbers)/(Total number of items)

Mean = 60/10 = 6

Again, Number 6 is occurring for 3 times, therefore Mode = 6. Answer

 

Example 2: A bucket contains 5 blue, 4 green and 5 red balls. Sudheer is asked to pick 2 balls randomly from the bucket without replacement and then one more ball is to be picked. What is the probability he picked 2 green balls and 1 blue ball?

Solution: Total number of balls = 14

Probability of drawing

1 green ball = 4/14

another green ball = 3/13

1 blue ball = 5/12

Probability of picking 2 green balls and 1 blue ball = 4/14 * 3/13 * 5/12 = 5/182.

 

Example 3: What is the probability that Ram will choose a marble at random and that it is not black if the bowl contains 3 red, 2 black and 5 green marbles.

Solution: Total number of marble = 10

Red and Green marbles = 8

Find the number of marbles that are not black and divide by the total number of marbles.

So P(not black) = (number of red or green marbles)/(total number of marbles)

= 8 /10

Practise This Question

Let a,b,cϵR. If f(x)=ax2+bx+c be such that a+b+c=3 and f(x+y)=f(x)+f(y)+xy, x, yϵR, then 10n=1 f(n) is equal to

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