Probability • Topic 1 of 2

Classical Definition of Probability

What is the classical definition of probability? Probability is the measure of how likely an event is to occur. The classical definition (also called theoretical probability) states:

P(E) = Number of favorable outcomes / Total number of possible outcomes

P(E) = n(E) / n(S)

where:

P(E) = probability of event E
n(E) = number of outcomes favorable to event E
n(S) = total number of all possible outcomes (sample space)

Key properties:

Probability is always between 0 and 1 (inclusive)
0 means impossible event (will never happen)
1 means certain event (will always happen)
Sum of probabilities of all possible outcomes = 1
P(not E) = 1 − P(E) (complementary event)

Real-life examples:

Tossing a coin: P(getting heads) = 1/2 = 0.5
Rolling a die: P(getting 4) = 1/6 ≈ 0.1667
Drawing an ace from a deck of 52 cards: P(ace) = 4/52 = 1/13

Important assumptions:

All outcomes are equally likely
The experiment is random (no bias)
Only classical probability is in Grade 10 syllabus (not experimental/statistical)

┌─────────────────────────────────────────────────────────────┐
│         CLASSICAL PROBABILITY - VISUAL REPRESENTATION        │
└─────────────────────────────────────────────────────────────┘

PROBABILITY SCALE:

    0                    0.5                    1
    │───────────────────────│───────────────────────│
    Impossible          Even Chance           Certain
    
    Examples:
    0 = P(sun rising in west)
    0.5 = P(getting heads on coin toss)
    1 = P(sun rising in east)


SAMPLE SPACE VISUALIZATION:

COIN TOSS:               DIE ROLL:

      ┌───┐                  ┌───┐
      │ H │                  │ 1 │
      └───┘                  └───┘
      ┌───┐                  ┌───┐
      │ T │                  │ 2 │
      └───┘                  └───┘
    n(S) = 2                ┌───┐
                            │ 3 │
                            └───┘
                            ┌───┐
                            │ 4 │
                            └───┘
                            ┌───┐
                            │ 5 │
                            └───┘
                            ┌───┐
                            │ 6 │
                            └───┘
                          n(S) = 6


PROBABILITY AS A FRACTION:

    P(E) = Favorable Outcomes / Total Outcomes
    
    Example: Drawing a red card from deck of 52 cards
    
    Total outcomes = 52 cards
    Favorable outcomes = 26 red cards (hearts + diamonds)
    
    P(red) = 26/52 = 1/2 = 0.5


COMPLEMENTARY EVENTS:

         P(E) + P(not E) = 1
    
    ┌─────────────────────────────────────────┐
    │              SAMPLE SPACE                │
    │  ┌─────────────┐  ┌─────────────────────┐│
    │  │             │  │                     ││
    │  │    Event    │  │   Complement        ││
    │  │      E      │  │      E'             ││
    │  │  P(E)       │  │  P(not E) = 1-P(E)  ││
    │  │             │  │                     ││
    │  └─────────────┘  └─────────────────────┘│
    └─────────────────────────────────────────┘

Solved Examples

Worked Example

A fair coin is tossed once. Find the probability of getting a head.

Solution

Step 1: Total possible outcomes = {H, T} → n(S) = 2
Step 2: Favorable outcomes (head) = {H} → n(E) = 1
Step 3: P(E) = n(E)/n(S) = 1/2

Answer: P(H) = 1/2 = 0.5

Worked Example

A die is rolled once. Find the probability of getting an even number.

Solution

Step 1: Total outcomes = {1,2,3,4,5,6} → n(S) = 6
Step 2: Even numbers = {2,4,6} → n(E) = 3
Step 3: P(even) = 3/6 = 1/2

Answer: P(even) = 1/2

Worked Example

One card is drawn from a well-shuffled deck of 52 playing cards. Find the probability that it is either a king or a queen.

Solution

Step 1: Total outcomes = 52
Step 2: Number of kings = 4, number of queens = 4
Step 3: Favorable outcomes = 4 + 4 = 8 (no overlap — a card cannot be both king and queen)
Step 4: P(king or queen) = 8/52 = 2/13

Answer: P(king or queen) = 2/13

Key Points

Classical probability: P(E) = Number of favorable outcomes / Total outcomes
Probability is always between 0 and 1 (inclusive)
Sum of probabilities of all outcomes = 1
P(not E) = 1 − P(E) (complement rule)
All outcomes must be equally likely for classical definition to apply
Probability can be expressed as fraction, decimal, or percentage

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Classical probability $P(E)=$

Explanation: Ratio of favourable to total.

Q2.The probability of a sure event is:

Explanation: $P(\text{sure})=1$.

Q3.The probability of an impossible event is:

Explanation: $P(\text{impossible})=0$.

Q4.For any event, $P(E)$ lies in:

Explanation: $0\le P(E)\le1$.

Practice more MCQs → 📝 Assignment · 35 marks