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.".
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Hierarchy of management that covers different levels of management
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Formulas of Probability :Class 12 maths
1.
2. 1. ๐ ๐ด โช ๐ต = ๐ ๐ด + ๐ ๐ต โ ๐ ๐ด โฉ ๐ต
2. If A and B are mutually exclusive, Aโฉ ๐ต = โ
3. If A and B are mutually exclusive, ๐ ๐ด โช ๐ต = ๐ ๐ด + ๐ ๐ต
4. A/B
๐๐๐๐๐๐๐
A given that B has occurred
3. 5. ๐ ๐ด
๐ต =
๐(๐ดโฉ๐ต)
๐(๐ต)
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
=
๐
1โ๐
Odds against A =
1โ๐
๐
8. A and B are said to be exhaustive if ๐ด โช ๐ต = ๐ where S is
the sample space
4. 9. If ๐ธ1, ๐ธ2,โโโโโโโ ๐ธ ๐ are n mutually exclusive and exhaustive events
associated with a sample space S and A is any event associated with S, then
๐ ๐ด = ๐ ๐ธ1 ๐ ๐ด
๐ธ1
+ ๐ ๐ธ2 ๐ ๐ด
๐ธ2
+โโโโโโ โ๐ ๐ธ ๐ ๐( ๐ด
๐ธ ๐
)
10. Bayesโ theorem
If ๐ธ1, ๐ธ2, ๐ธ3are n mutually exclusive and exhaustive events associated with
a random experiment and A is any event associated with S, then
๐
๐ธ1
๐ด =
๐ ๐ธ1 ๐( ๐ด
๐ธ1)
๐ ๐ธ1 ๐ ๐ด
๐ธ1
+ ๐ ๐ธ2 ๐ ๐ด
๐ธ2
+ ๐ ๐ธ3 ๐( ๐ด
๐ธ3
)
11. A random variable is a variable whose values are determined by chance.
12. Sum of the probabilities of a random variable is 1
๐๐ = 1
5. 13. Mean of a random variable ๐ = ๐ฅ๐ ๐ฅ
14. Variance of a random variable ๐2
= ๐๐ ๐ฅ๐
2
โ ๐2
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 ) = ๐ ๐ถ ๐
๐ ๐
๐ ๐โ๐
17. A Binomial distribution is (๐ + ๐) ๐
since the successive probabilities are the
terms of the binomial expansion
18.For a binomial distribution, mean = np
19.Variance = npq