Grades Grade 7 Statistics & ProbabilityProbability of Simple & Compound Events

Probability of Simple & Compound Events

🎲 Statistics & Probability

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Probability of Simple & Compound Events

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

The theoretical probability of an event is the ratio of favorable outcomes to total equally likely outcomes. For compound events (two or more events), use multiplication rules and consider whether events are independent.

P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}

P(A \text{ and } B) = P(A) \times P(B) \quad (\text{if A and B are independent})

🎯Rolling a die and flipping a coin

What is the probability of rolling a 3 AND flipping heads?

P(rolling 3) = 1/6
P(heads) = 1/2

These are independent events:
P(3 and heads) = (1/6) × (1/2) = 1/12

P(3 \cap H) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}

Building a sample space for compound events:

1List all outcomes for the first event

2Pair each with all outcomes of the second event

3Count total pairs (= size of sample space)

4Count pairs where the desired outcome occurs

5Divide: favorable ÷ total

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Remember This!

The probability of an event NOT occurring is 1 − P(event). This is called the complement. P(at least one heads in 3 flips) = 1 − P(all tails) = 1 − (1/2)³ = 7/8.

✏️ Try It!

A bag has 3 red, 2 blue, and 5 green marbles. What is the probability of drawing a red marble?

Practice with CalcVerse

🎲Dice & Coin Simulator

Take Quiz 📝 — 25 Questions