ICSE : Probability

Probability practice sums👈

1. What is Probability?

Probability is the measure of how likely an event is to occur.

📌 Formula:

$\text{Probability of an event (E)} = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

Probability is always a number between 0 and 1.
0 means impossible, 1 means certain.

🔹 2. Important Terms

Term	Meaning
Experiment	An action like tossing a coin or rolling a die
Outcome	Result of a single trial (e.g., getting a head)
Sample Space (S)	Set of all possible outcomes
Favourable Outcome	The outcomes which support the required event
Event (E)	A subset of the sample space

🔹 3. Example Sample Spaces

Tossing a coin → {H, T}
Tossing 2 coins → {HH, HT, TH, TT}
Rolling a die → {1, 2, 3, 4, 5, 6}
Drawing a card from a pack:
- Total = 52 cards
- Red cards = 26, Black cards = 26
- Face cards = 12 (Jack, Queen, King of each suit)
- Aces = 4

52 Cards

│

┌────────────────────────────┐

│ │

26 Red Cards 26 Black Cards

(♥ Hearts & ♦ Diamonds) (♣ Clubs & ♠ Spades)

│ │

┌───┴────┐ ┌─────┴────┐

│ │ │ │

13 Hearts 13 Diamonds 13 Clubs 13 Spades

All Face Cards (J, Q, K) — 12 Total

4 Jacks, 4 Queens, 4 Kings

Other Special Cards:

- Aces = 4 (One in each suit)

Sample Space of Two Dice in Row-Column Table

Each cell represents the ordered pair $(i, j)$ where:

i = number on Die 1 (row)
j = number on Die 2 (column)

Die 1 ↓ / Die 2 →	1	2	3	4	5	6
1	(1,1)	(1,2)	(1,3)	(1,4)	(1,5)	(1,6)
2	(2,1)	(2,2)	(2,3)	(2,4)	(2,5)	(2,6)
3	(3,1)	(3,2)	(3,3)	(3,4)	(3,5)	(3,6)
4	(4,1)	(4,2)	(4,3)	(4,4)	(4,5)	(4,6)
5	(5,1)	(5,2)	(5,3)	(5,4)	(5,5)	(5,6)
6	(6,1)	(6,2)	(6,3)	(6,4)	(6,5)	(6,6)

ICSE

Probability