Probability basics

PROBABILITY Presented by:
Savi Arora

BASIC TERMS
Probability: Measure if likeliness than an event will
occur.
Sample Space: Set of all possible outcomes.
Event: Any subset of any outcomes of any
experiment.
Mutually exclusive event: Event which cannot occur
together.
Dependent and Independent events.

PROBABILITY MANTRA
outcomepossibleofnoTotal
outcomefavourableofNo
EP )(

TODAY WE WILL PLAY WITH
Coins
Dice
Cards
&
A bag full of colorful balls.

PRACTICE – 1
A dice is thrown, find probability
P(even no) =
P(no less than 3) =
P(not 3) =
In a deck of 52 cards
P(ace) =
P(red card) =
P(face card) =

CLARIFICATION: AND – OR
)()( BAPBorAP 
)()( BAPBandAP  A B

RULE OF ADDITION
Mutually exclusive event:
Not Mutually exclusive event:
)()()( BPAPAorBP 
)()()()( BandAPBPAPAorBP 

PRACTICE – 2
A Dice is thrown once:
P( 2 or 3) =
P(multiple of 2 or multiple of 3) =
In Deck of 52 cards
P(red or face) =
One ball drawn: Bag contains – 10 Red, 15 Yellow, 25
Green
P( Yellow or Green) =

RULE OF MULTIPLICATION
Independent Events:
Dependent Event:
)()()( BPAPBandAP 
)|()()( ABPAPBandAP 
)|()()( BAPBPBandAP Or

PRACTICE – 3
Bag contains – 10 Red, 15 Yellow, 25 Green
Two balls drawn (with replacement):
P(1st Red, 2nd Yellow) =
P(Both Red) =
P(One Red, one Yellow) =
Two balls drawn (without replacement):
P(1st Red, 2nd Yellow) =
P(Both Red) =
P(One Red, one Yellow) =

COIN
Two unbiased coins are tossed simultaneously:
P(one head) =
P(atleast one head) =
P(No head) =
P(one Head one Tail) =

COIN
Three unbiased coins are tossed simultaneously:
P(two head) =
P(at least two head) =
P(at most two head) =
P(All head) =

COIN
Four or More Coins are tossed??
You need Binomial for that.

PERMUTATION & COMBINATION
Permutation: “one or more elements of a set where order does
matter”
Combination: “one or more elements of a set where order does not
matter”
For e.g.: Take 3 Letters – ABCPermutation of 2 of
these letter: 3P2 = 6
AB BA
AC CA
BC CB
Combination of 2 of
these letter: 3C2 = 3
AB
AC
BC
Now Take 4 : Letter – ABCD
And write Permutation & Combination of 3 of th

P&C
Permutation
Combination
3 𝐶2 =
3!
3 − 2 ! 2!
= 3n 𝐶 𝑟 =
𝑛!
𝑛 − 𝑟 ! 𝑟!
3 𝑃2 =
3!
3−2 !
= 6
n 𝑃 𝑟 =
𝑛!
𝑛 − 𝑟 !
*We will focus majorly on COMBINATIO

PRACTICE – 4
Bag is Back : 10 Red, 15 Yellow, 25 Green
Three bolls drawn at random, find:
P(each different color) =
P(2 red 1 green) =
P(exactly 2 green) =
P(at least 2 green) =
P(at most 2 green) =

PRACTICE – 4
Bag is Back : 10 Red, 15 Yellow, 25 Green
Two draws of three balls each are drawn at random (with
replacement)
P(1st three Red, 2nd three yellow) =
P(all different color, all different color) =
P(one draws three red, other draws three yellow) =
*Wanna try without replacement??

BAYES’ THEOREM
What is the probability of outcome A given that outcome B has
already occurred. i.e. P(A|B)
)'().'|()().|(
)().|(
)|(
APABPAPABP
APABP
BAP


n.,...2,1,=k,
)B|P(A×)P(B
)B|P(A×)P(B
=A)|P(B
1
ii
ik
k

n
i
Believe me! You don’t need to remember this, if you Still go with your Probability Mantra a

PRACTICE – 5
A bulb is manufactured in one of the three machines X,Y,Z.
The machines produce in capacity: X – 30%, Y – 30%, Z – 40%.
Probability of bulb found defective in machine X – 10%, Y – 15%,
Z – 20%.
A bulb is drawn at random and is found to be defective.
What is the probability that the bulb was produced in Machine
Y??

THANK YOU
Queries are welcomed.

Probability basics

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Probability basics