I present to you all the formulae of probability needed for classes 11 and 12, ISC, CBSE curriculum. These are covered in my course "Probability for class 12: questions with solutions.".
The entire course is available for Rs 1099 only.
Maths Class 12 Probability Project PresentationAaditya Pandey
Class 12 Maths Presentation on Probability. Mathematics Project Class 12th on Chapter 13 Probability. Project in English. Chapter 13 Up to 2020-21 Revised syllabus up to Baye's Theorem.
History behind the
development of the concept
In 1654, a gambler Chevalier De Metre approached the well known Mathematician Blaise Pascal for certain dice problem. Pascal became interested in these problems and discussed it further with Pierre de Fermat. Both of them solved these problems independently. Since then this concept gained limelight.
Basic Things About The Concept
Probability is used to quantify an attitude of mind towards some uncertain proposition.
The higher the probability of an event, the more certain we are that the event will occur.
Maths Class 12 Probability Project PresentationAaditya Pandey
Class 12 Maths Presentation on Probability. Mathematics Project Class 12th on Chapter 13 Probability. Project in English. Chapter 13 Up to 2020-21 Revised syllabus up to Baye's Theorem.
History behind the
development of the concept
In 1654, a gambler Chevalier De Metre approached the well known Mathematician Blaise Pascal for certain dice problem. Pascal became interested in these problems and discussed it further with Pierre de Fermat. Both of them solved these problems independently. Since then this concept gained limelight.
Basic Things About The Concept
Probability is used to quantify an attitude of mind towards some uncertain proposition.
The higher the probability of an event, the more certain we are that the event will occur.
quantitative aptitude, maths
applicable to
Common Aptitude Test (CAT)
Bank Competitive Exam
UPSC Competitive Exams
SSC Competitive Exams
Defence Competitive Exams
L.I.C/ G. I.C Competitive Exams
Railway Competitive Exam
University Grants Commission (UGC)
Career Aptitude Test (IT Companies) and etc.
quantitative aptitude, maths
applicable to
Common Aptitude Test (CAT)
Bank Competitive Exam
UPSC Competitive Exams
SSC Competitive Exams
Defence Competitive Exams
L.I.C/ G. I.C Competitive Exams
Railway Competitive Exam
University Grants Commission (UGC)
Career Aptitude Test (IT Companies) and etc.
It gives detail description about probability, types of probability, difference between mutually exclusive events and independent events, difference between conditional and unconditional probability and Bayes' theorem
Probability is the way of expressing knowledge of belief that an event will occur on chance.
Did You Know? Probability originated from the Latin word meaning approval.
Make use of the PPT to have a better understanding of Probability.
Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.[note 1][1][2] The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ('heads' and 'tails') are both equally probable; the probability of 'heads' equals the probability of 'tails'; and since no other outcomes are possible, the probability of either 'heads' or 'tails' is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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Formulas of Probability :Class 12 maths
1.
2. 1. 𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃 𝐴 ∩ 𝐵
2. If A and B are mutually exclusive, A∩ 𝐵 = ∅
3. If A and B are mutually exclusive, 𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃 𝐵
4. A/B
𝑖𝑚𝑝𝑙𝑖𝑒𝑠
A given that B has occurred
3. 5. 𝑃 𝐴
𝐵 =
𝑃(𝐴∩𝐵)
𝑃(𝐵)
6. A and B are independent events, if the occurrence of A does
not affect the occurrence of B
7. If A is any event with probability p, then odds in favour of A
=
𝑝
1−𝑝
Odds against A =
1−𝑝
𝑝
8. A and B are said to be exhaustive if 𝐴 ∪ 𝐵 = 𝑆 where S is
the sample space
4. 9. If 𝐸1, 𝐸2,−−−−−−− 𝐸 𝑛 are n mutually exclusive and exhaustive events
associated with a sample space S and A is any event associated with S, then
𝑃 𝐴 = 𝑃 𝐸1 𝑃 𝐴
𝐸1
+ 𝑃 𝐸2 𝑃 𝐴
𝐸2
+−−−−−− −𝑃 𝐸 𝑛 𝑃( 𝐴
𝐸 𝑛
)
10. Bayes’ theorem
If 𝐸1, 𝐸2, 𝐸3are n mutually exclusive and exhaustive events associated with
a random experiment and A is any event associated with S, then
𝑃
𝐸1
𝐴 =
𝑃 𝐸1 𝑃( 𝐴
𝐸1)
𝑃 𝐸1 𝑃 𝐴
𝐸1
+ 𝑃 𝐸2 𝑃 𝐴
𝐸2
+ 𝑃 𝐸3 𝑃( 𝐴
𝐸3
)
11. A random variable is a variable whose values are determined by chance.
12. Sum of the probabilities of a random variable is 1
𝑝𝑖 = 1
5. 13. Mean of a random variable 𝜇 = 𝑥𝑝 𝑥
14. Variance of a random variable 𝜎2
= 𝑝𝑖 𝑥𝑖
2
− 𝜇2
15. A Binomial trial is a trial in which
i. n is finite and is defined before the experiment
ii. each trial has only 2 possible outcomes, success and failure
iii. the result of any trial is independent of the result of other trials.
iv. the probability of success does not change from trial to trial
eg. Tossing a fair coin 10 times and recording number of heads
Tossing a biased coin 10 times and recording number of heads.
Rolling 2 dice 4 times and recording the number of times we get a total of 5
Drawing a card 10 times and determining if it is a diamond, replacing the card after
each trial.
6. 16 For a binomial distribution, if p denotes success and q
denoted failure
P(X= r ) = 𝑛 𝐶 𝑟
𝑝 𝑟
𝑞 𝑛−𝑟
17. A Binomial distribution is (𝑞 + 𝑝) 𝑛
since the successive probabilities are the
terms of the binomial expansion
18.For a binomial distribution, mean = np
19.Variance = npq