Probability

Front 1

Collection of sample point is known as

Back 1

Sample space

Front 2

Event

Back 2

Each subset of a sample space is called an event

Front 3

Null event

Back 3

No sample point

Front 4

Sure event

Back 4

Event which is sure to occur

Front 5

Equally likely events

Back 5

When we don't exist the happening of an event in performance to the other

Front 6

Mutually exclusive event

Back 6

2 event associated with an experiment are said to be mutually exclusive, if both the events cannot occur simultaneously in same trial

Front 7

Event A or B

Back 7

AUB

Front 8

At least one of them

Back 8

A&B

Front 9

Event A and B

Back 9

A∆B

Ulta U =∆

Front 10

Compliment event

Back 10

A' ; all the element of sample space which are not in A.

Also knowns as mutually exclusive events

Front 11

Atleast

Back 11

Kam se kam

Front 12

At most

Back 12

Jyada se jyada

Front 13

P(A)+P(A')

Back 13

= 1

Front 14

Odds in favourable of an event E

Back 14

Ratio of

No. of favourable case to the no. of unfavourable case

Front 15

Odds against of an event E

Back 15

Ratio of

No. of unfavourable case to the No. of favourable case

Front 16

If coin is tossed two times, the no. of sample space is

Back 16

2ⁿ

Front 17

P(AUB) =

Back 17

P(A) + P(B) - P(A∆B)

Front 18

Default & Mentioned ball drawn

Back 18

Together & One by one respectively

Front 19

Balls drawn one by one

Back 19

Fraction method

Front 20

Balls drawn together

Back 20

Combination method

Front 21

Arrangement

N person sitting in a row

Back 21

n! no. of ways

Front 22

Arrangement

N person sitting in a round table

Back 22

n-1! no. of ways

Front 23

Condition probability

P(A/B)

Back 23

P(A∆B)/P(B)

Front 24

Independent event

P(A∆B) =

Back 24

P(A) × P(B)

Front 25

ⁿCr

Back 25

n!/r!×(n-r)!

Front 26

ⁿCn

Back 26

1

Front 27

ⁿCo

Back 27

1

Front 28

ⁿCr

Back 28

ⁿC(n-r)

Front 29

Binomial distribution formula

Back 29

P(x=r) = ⁿCr p^r q^(n-1)

p= probability of success

q= probability of failure

p+q = 1

n= no. of trial

r= desired no. of success

Front 30

Mean of BD

Back 30

np

Front 31

Variance of BD

Back 31

npq

Front 32

In BD p=q

Back 32

Symmetrical histogram

Front 33

In BD p is not equal to q

Back 33

Unsymmetrical histogram

Front 34

Poisson Disturbances formula

Back 34

P(x=r) = (e^-† {†}^r)/r!

† = lemda = np

Front 35

Mean § & variance of PD

Back 35

Lemda

Front 36

Note for PD

Back 36

It is positively skewed

Front 37

Normal distribution formula

Back 37

P = [e^{-(x-u)²/2§z}/§√2π]

§ → sigma

u = mean

Front 38

Mean, § and variance of ND

Back 38

np

√npq

npq

Front 39

Standard deviation §

Back 39

√npq

Front 40

z in ND

Back 40

z= normal variate

x= binomial variate

z= x-u /§

Front 41

Note for ND

Back 41

It is always symmetrical

Skewness is 0

Front 42

Relation between mean & variance in ND

Back 42

u = 4/5 §

Front 43

Relation btw Standard deviation § & variance.

Back 43

§² = variance

Front 44

Coefficient of variance

Back 44

Standard deviation / mean

u = mean

Front 45

Symmetrical distribution

Back 45

Mean = Median = mode

Front 46

Unsymmetrical distribution

Back 46

Mode = 3 Median - 2 Mean

Front 47

For positively skewed data

Back 47

Mode > Median > Mean

Front 48

For 0 skewness data

Back 48

Mean = Median = mode

Front 49

Conditional probability

Back 49

P(E1/E2) = P(E1∆E2)/P(E2)

P(E2/E1) = P(E1∆E2)/P(E1)

Front 50

§ of BD

Back 50

√npq

Front 51

Mean

Back 51

Sum of observation / no. of observation

Front 52

Mean for group data

Back 52

€( fi × xi)/ €fi

Front 53

Short cut method (mean)

Back 53

A + [€(fi × di)/€fi]

Front 54

Step deviation method (Mean)

Back 54

A + [{€(fi × ui)/€fi} × h]

Front 55

Median

Back 55

= L + ( {€fi/2 - C} / f ) × h

Front 56

Mode

Back 56

L + ({f1-f2} / {2f1 - fo -f2}) × h