Probability (Intro) • Topic 1 of 2

Basic Probability & Likelihood Scale

Probability measures how likely an event is to occur. It ranges from 0 (impossible) to 1 (certain).

Formula: P(event) = Number of favorable outcomes / Total number of possible outcomes

Probability Value	Meaning	Example
0	Impossible	Rolling a 7 on a standard die
0 to 0.5	Unlikely	Rolling a 1 on a die (1/6)
0.5	Equally likely	Flipping heads on a coin
0.5 to 1	Likely	Drawing a red card from a deck
1	Certain	Sun rising tomorrow

The sum of probabilities of all possible outcomes always equals 1.

LIKELIHOOD SCALE:

0          0.25        0.5        0.75        1
|----------|-----------|----------|----------|
Impossible Unlikely   Equal     Likely    Certain

SPINNER EXAMPLE (8 equal sections, 1-8):
  P(odd number)    = 4/8 = 1/2 = 0.5
  P(number > 6)    = 2/8 = 1/4 = 0.25
  P(multiple of 4) = 2/8 = 1/4 = 0.25
  P(number = 9)    = 0/8 = 0 (impossible)

Solved Examples

Worked Example

A bag has 3 red, 2 blue, 5 green marbles. Find P(red), P(blue), P(black).

SolutionTotal = 10. P(red)=3/10=0.3. P(blue)=2/10=0.2. P(black)=0/10=0 (no black marbles).

Worked Example

Roll a fair die once. Find P(4), P(even), P(less than 3), P(greater than 6).

SolutionP(4)=1/6. P(even)=3/6=1/2. P(<3)=2/6=1/3 (for 1 or 2). P(>6)=0/6=0.

Worked Example

A deck has 52 cards. Find P(King) and P(Heart).

SolutionP(King)=4/52=1/13. P(Heart)=13/52=1/4.

Key Points

Probability is always between 0 and 1 (inclusive)
P(event) = favorable outcomes / total outcomes
Sum of all outcome probabilities = 1
P(not A) = 1 - P(A)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.A probability lies between:

Explanation: $0\le P\le1$.

Q2.A certain event has probability:

Explanation: $1$.

Q3.An impossible event has probability:

Explanation: $0$.

Q4.$P(\text{head})$ on a fair coin is:

Explanation: $\tfrac12$.

Practice more MCQs → 📝 Assignment · 35 marks