Probability

📐

Foundation

What is Probability?

Learn the formula, the range of probability, and how sample spaces work.

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📖

Key Vocabulary

Technical Terms

All 9 terms from your textbook — Experiment, Sample Space, Events and more.

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🪙

Interactive

Toss the Coin

Flip a 3D coin and see probability in action — Heads or Tails, each P = ½.

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🧠

Practice

Solve Step-by-Step

8 guided problems — answer each step and build your solution one piece at a time.

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Probability measures the likelihood that an event will occur. It is always a number between 0 and 1.

P(Event) = Number of Favourable OutcomesTotal Number of Possible Outcomes

P = 0 → Impossible—P = ½ → Equal chance—P = 1 → Certain

Coin Toss — Sample Space S

H — HeadsT — Tails

S = {H, T} | n(S) = 2
P(H) = 1/2 = 0.5 | P(T) = 1/2 = 0.5

Dice Roll — Sample Space S

123456

S = {1, 2, 3, 4, 5, 6} | n(S) = 6
P(any face) = 1/6 ≈ 0.167

Probability Scale

0 — Impossible0.25 — Unlikely0.5 — Equal0.75 — Likely1 — Certain

a

Term (a)

Experiment

A result or outcome that cannot be predicted in advance.

Examples: Tossing a coin · Rolling a die · Drawing a card

b

Term (b)

Random Experiment

An experiment whose outcomes cannot be predicted with certainty.

Coin toss → H or T, unpredictable

c

Term (c)

Outcomes

The results of a random experiment.

Coin → {H, T} | Die → {1, 2, 3, 4, 5, 6}

d

Term (d)

Equally Likely Outcomes

Outcomes where each has an equal chance of occurring.

P(H) = P(T) = 1/2 for a fair coin

e

Term (e)

Sample Space

The set of all possible outcomes, denoted S. Count = n(S).

Coin: S={H,T}, n(S)=2 | Die: S={1–6}, n(S)=6

f

Term (f)

Event

Each outcome of a random experiment, denoted E.

E = {H} | P(E) = 1/2

g

Term (g)

Mutually Exclusive Events

Events that cannot occur at the same time.

H and T cannot occur together in one toss

h

Term (h)

Favourable Outcomes

The outcomes that result in a specific event happening.

P(≥4 on die)=3/6=1/2 (favourable: 4,5,6)

i

Term (i)

Elementary Event

Each single possible outcome of a sample space.

Die elementary events: {1},{2},{3},{4},{5},{6}

Click the button to toss!

Probability of Each Outcome

🟡 Heads (H)

12=0.5

🔵 Tails (T)

12=0.5

Using the Formula

P(Heads) = Favourable / Total
= 1 / 2 = 0.5

P(Tails) = Favourable / Total
= 1 / 2 = 0.5

Sample Space S = {H, T} | n(S) = 2

Toss History

No tosses yet…