Probability Notes for JKSSB Competitive Examinations

(Basic to Advanced with Practice Questions – Home Academy)

1. Introduction to Probability

Probability is the branch of mathematics that deals with the chance of occurrence of an event.

Formula:

$$Probability$$

Where:

P(E) = Probability of event E

n(E) = Number of favourable outcomes
n(S) = Total outcomes (Sample Space)

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2. Important Terms

(a) Experiment

An action that produces outcomes.

Examples:

Tossing a coin

Throwing a die
Drawing a card

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(b) Trial
Performing an experiment once.
Example:
One coin toss = One trial.

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(c) Outcome
Result of an experiment.
Example:
Coin Toss → H (Head) or T (Tail)

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(d) Sample Space (S)
Set of all possible outcomes.
Examples:
Coin:
S={H,T}
Die:
S={1,2,3,4,5,6}

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(e) Event
A set of favourable outcomes.
Example:
Getting an even number on a die.
E={2,4,6}

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3. Types of Events
1. Sure Event
Probability = 1
Example:
Getting a number less than 7 on a die.

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2. Impossible Event
Probability = 0
Example:
Getting 8 on a die.

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3. Equally Likely Events
All outcomes have equal chance.
Example:
Fair coin.

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4. Mutually Exclusive Events
Cannot happen together.
Example:
Getting 2 and 5 in one die throw.

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5. Independent Events
Occurrence of one does not affect another.
Example:
Two coin tosses.

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4. Probability of Coin Toss
One Coin

Outcome	Probability
Head	1/2
Tail	1/2

Two CoinsSample Space:
S={HH,HT,TH,TT}S=\{HH, HT, TH, TT\}
Total outcomes = 4
Probability of:
Two Heads = 1/4
One Head = 2/4 = 1/2
No Head = 1/4

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Three Coins
Total outcomes:
23=82^3=8

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5. Probability of Dice
A die has 6 faces.
S={1,2,3,4,5,6}S=\{1,2,3,4,5,6\}
Example:
Probability of getting an even number:
Even numbers = 2,4,6
P=3/6=1/2

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6. Probability of Cards
A deck contains:
Total Cards = 52
Red Cards = 26
Black Cards = 26
Hearts = 13
Diamonds = 13
Clubs = 13
Spades = 13
Face Cards:
Jack = 4
Queen = 4
King = 4
Total Face Cards = 12

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Example:
Probability of drawing a King:
P=4/52=1/13

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7. Complementary Probability
P(A′)=1−P(A)P(A')=1-P(A)
Example:
Probability of getting an even number on die:
P(E)=3/6
Probability of not getting even:
P(E′)=1−36=1/2

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8. Addition Rule
For mutually exclusive events:
P(A∪B)=P(A)+P(B)P(A\cup B)=P(A)+P(B)
Example:
Probability of getting 1 or 2 on a die:
P=1/6+1/6=2/6=1/3

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9. Multiplication Rule
For independent events:
P(A∩B)=P(A)×P(B)P(A\cap B)=P(A)\times P(B)
Example:
Two Heads in two coin tosses:
P=12×12=1/4

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10. Conditional Probability
P(A∣B)=P(A∩B)P(B)P(A|B)
This is important for higher-level exams.

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Important Probability Formulas

Formula	Expression
Basic Probability	$P(E)=\frac{n(E)}{n(S)}$
Complement	$P(A')=1-P(A)$
Addition	$P(A+B)=P(A)+P(B)$
Multiplication	$P(A\cap B)=P(A)P(B)$
Conditional	(P(A

Short Tricks for JKSSBCoins
n Coins:
Total Outcomes=2nTotal\ Outcomes=2^n

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Dice
n Dice:
Total Outcomes=6nTotal\ Outcomes=6^n

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Cards
Total Cards = 52

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Practice Questions (Solved)
Q1.
A coin is tossed once. Find probability of Head.
Solution:
P(H)=1/2

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Q2.
Find probability of getting an odd number on a die.
Odd numbers = 1,3,5
P=36=1/2

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Q3.
Two coins are tossed. Find probability of exactly one Head.
Sample Space:
HH, HT, TH, TT
Favourable = HT, TH
P=2/4= 1/2

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Q4.
A card is drawn. Find probability of Ace.
P=4/52=1/13

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Q5.
Two dice are thrown. Probability of sum = 7.
Favourable:
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
Total outcomes = 36
P=6/36=1/6

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JKSSB MCQs
1. Probability always lies between:
A) 0 and 1
B) 1 and 2
C) -1 and 1
D) 0 and 2
Answer: A
2. Probability of sure event is:
A) 0
B) 1
C) 2
D) 1/2
Answer: B
3. Probability of impossible event is:
A) 0
B) 1
C) 1/2
D) 2
Answer: A
4. Total outcomes when 3 coins are tossed:
A) 6
B) 8
C) 9
D) 12
Answer: B
5. Total outcomes when 2 dice are thrown:
A) 12
B) 24
C) 36
D) 18
Answer: C

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Statement Type Questions
Statement I:
Probability of a sure event is 1.
Statement II:
Probability of an impossible event is 0.
A) Both true
B) Both false
C) Only I true
D) Only II true
Answer: A

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Statement I:
A fair coin has two equally likely outcomes.
Statement II:
Probability of Head is 1/3.
Answer: Only Statement I is true.

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Previous Exam Level Questions
Two dice are thrown. Find probability of getting sum greater than 9.
A card is drawn. Find probability of a face card.
Three coins are tossed. Find probability of exactly two Heads.
One die is thrown. Find probability of prime number.
A bag contains 5 red and 3 blue balls. Find probability of selecting a red ball.