Probability of an event
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). When all outcomes are equally likely:
| Event | Probability |
|---|---|
| Getting a head on a coin | 1/2 |
| Rolling a 4 on a die | 1/6 |
| Rolling an even number | 3/6 = 1/2 |
| Drawing a red card from a deck | 26/52 = 1/2 |
The probability that an event does not happen is 1 − P(E). The total of the probabilities of all outcomes is 1.
Combined events
| Type | Rule | Example |
|---|---|---|
| Mutually exclusive (cannot both happen) | P(A or B) = P(A) + P(B) | A die shows 1 or 6: 1/6 + 1/6 = 1/3 |
| Independent (one does not affect the other) | P(A and B) = P(A) × P(B) | Two heads in two tosses: 1/2 × 1/2 = 1/4 |
| General | P(A or B) = P(A) + P(B) − P(A and B) | For overlapping events |
Worked exampleTwo events
A bag has 3 red and 5 blue balls. One is drawn, replaced, and another drawn. Find the probability that both are red.
- The draws are independent.
- Multiply.
Answer: The probability is 9/64.
Try itRepeating an event
An event has the probability p each time. Choose p and the number of trials.
Key terms
- Probability
- A measure of the chance of an event, between 0 and 1.
- Outcome
- One possible result of an experiment.
- Independent events
- Events where one does not affect the other.
- Mutually exclusive
- Events that cannot happen together.
Summary
- P(E) = favourable ÷ total outcomes.
- P(not E) = 1 − P(E).
- For independent events multiply; for exclusive events add.
- Probabilities always lie between 0 and 1.