Probability – Grade 9 Notes
1. Surfaces of a Coin
A coin has two surfaces: Head and Tail.
When tossed, it may land on either surface.
2. Faces of a Dice
A standard dice is cubical with 6 faces, numbered 1 to 6.
Each face can appear when the dice is thrown.
3. Colours of Playing Cards
A standard deck has 52 cards.
There are two colours: Red (Hearts & Diamonds) and Black (Clubs & Spades).
4. Probability in Daily Life
Probability measures the chance of an event happening.
Example: Clouds in the sky may indicate the possibility of rain.
Probability helps in predicting uncertain events.
5. Key Terms in Probability
Experiment
An action performed to observe outcomes.
Example: Tossing a coin, rolling a dice, drawing a card.
Random Experiment
An experiment where the outcome cannot be predicted exactly.
Example: Tossing a dice or coin.
Outcomes
The result of an experiment.
Example: Coin toss → Head (H) or Tail (T).
Sample Space (S)
The set of all possible outcomes.
Example: Dice → S = {1, 2, 3, 4, 5, 6}.
Event (E)
Any subset of the sample space.
Example: Dice → Even numbers → {2, 4, 6}.
Sample Point
Each individual outcome of an experiment.
Example: Dice → 1, 2, 3, 4, 5, 6.
Elementary Event
An event consisting of only one outcome.
Example: Rolling a 3 → {3}.
Equally Likely Outcomes
Outcomes with equal chance of occurrence.
Example: Coin → Probability of Head = Probability of Tail = 1/2.
Favourable Outcomes
Outcomes that are desired for a specific event.
Probability Formula
Probability of an event E = Number of favourable outcomes / Total number of outcomes
P(E) = n(E) / n(S)
6. Examples of Probability
Example 1 – Coin Toss
Sample space S = {H, T}
Favourable outcome = {H}
Probability of Head = 1/2
Example 2 – Dice Roll
Sample space S = {1, 2, 3, 4, 5, 6}
Favourable outcome = {3}
Probability of 3 = 1/6
Example 3 – Card Draw (King)
Total cards = 52
Number of Kings = 4
Probability of King = 4/52 = 1/13
Example 4 – Day of the Week
Total days = 7
Probability of Sunday = 1/7
Example 5 – Birthday on Saturday
Total days = 7
Probability = 1/7
Example 6 – Marbles in a Bag
Bag: 2 Red, 3 Black, 4 Green → Total = 9
Probability of Red = 2/9
Probability of Green = 4/9
Example 7 – Prime Number Marbles
10 marbles numbered 1 to 10
Primes = {2, 3, 5, 7} → 4 marbles
Probability = 4/10
7. Probability Scale
Probability always lies between 0 and 1
P(E) = 1 – P(not E)
Example – Spinner
Spinner has Green, Yellow, Black sectors
Probability of Green = 1/3
Probability of not Green = 2/3
8. Empirical Probability
Based on actual experiments
Formula: Probability = Number of favourable outcomes / Total number of experiments
Example – Coin Toss
Toss coin 50 times: Head = 23, Tail = 27
Probability of Head = 23/50
Probability of Tail = 27/50
Example – Bricks
Total bricks = 2000
Probability of breaking = 0.1 → Probability of non-breaking = 0.9
Non-breaking bricks = 2000 × 0.9 = 1800
9. Important Solved Exercises (Stepwise)
1. Probability of Ace from deck
Total cards = 52
Favourable outcomes (Ace) = 4
Probability = 4/52 = 1/13
2. Probability of Dice Roll
P(2) = 1/6, P(3) = 1/6
3. Probability of child born on Sunday
Total days = 7, Favourable = 1
Probability = 1/7
4. Probability of Black Marble
Bag: 2 Blue, 3 Black, 5 Red → Total = 10
Probability of Black = 3/10
Probability of not Black = 7/10
5. Cards numbered 2–25
Multiples of 3 = 8 → Probability = 8/24 = 1/3
Even numbers = 12 → Probability = 12/24 = 1/2
6. Probability of selecting a girl
Total students = 50, Girls = 28
Probability = 28/50 = 14/25
7. Probability of English-speaking student
Total students = 35, Speak English = 25
Probability = 25/35 = 5/7
8. Two Coins Tossed
Total outcomes = 4 → {HH, HT, TH, TT}
Two Heads → 1/4
Two Tails → 1/4
One Head, One Tail → 1/2
9. Dice Outcomes
Face 5 → 1/6
Even → 3/6 = 1/2
Odd → 3/6 = 1/2
10. Dice Rolled 60 Times
Outcomes: 1(8), 2(9), 3(13), 4(15), 5(11), 6(4) → Total = 60
Probability of 4 = 15/60 = 1/4
Probability >5 → Only 6 → 4/60 = 1/15
Probability <3 → 1+2 = 8+9=17 → 17/60
Probability <7 → All numbers = 60/60 = 1
11. Probability of boy among newborns
Total babies = 100, Daughters = 35 → Boys = 65
Probability = 65/100 = 13/20
12. Daily Events Probability
High probability → Rainfall in monsoon
Low probability → Snow in summer
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