## Probability

Relative frequency

100 teenagers were asked what their favourite type of movie was and the results were recorded in a frequency table.

The relative frequency is the FRACTION or PROPORTION of people in that particular category.

e.g. 15 out of the 100 teenagers liked action movies so the relative frequency of action movies is 15/100 = 0.15

 Type of movie Frequency Relative frequency Fraction Decimal Percentage Action 15 15/100 0.15 15% Comedy 35 35/100 0.35 35% Drama 10 10/100 0.1 10% Horror 40 40/100 0.4 40% Total 100 1 1 100%

Based on these results it is more likely that the next person asked would like horror or comedy movies as they have the highest relative frequencies.

How likely an event is to happen can be predicted by its relative frequency.

 Relative frequency Likelihood of event happening Above 90% Very likely to happen Above 50% Likely to happen Below 50% Unlikely to happen Below 10% Very unlikely to happen

### Probability

• Probabilities are expressed as fractions, decimal fractions or percentages.
• An outcome is the result of an action such as throwing a die or picking a card from a pack.
• For equally likely outcomes, the probability of the event E occurring is given by:

Probability of event E happening =

 Example 1 Answer When a die is tossed, what is the probability that a 5 or a 6 will face up? Total six possible outcomes = {1, 2, 3, 4, 5, 6} Required two outcomes= {5, 6} P(E) = 2⁄6 = 1⁄3 Example 2 Answer A card is picked from a normal pack of 52. What is the probability the card will be a heart? There are 52 cards in a pack. There are 13 hearts. P(Heart) = 13/52 = 0.25

Probabilities will always be in the range from 0 to 1.
e.g. 0 ≤ P(E) ≤ 1

If the probability of an event happening is 0, the event cannot occur.

If the probability of an event happening is 1, the event is certain to occur.

e.g. P(throwing a six-sided die and scoring a 7) = 0

P(throwing a six-sided die and scoring less than 7) = 1

See an activity involving probabilities when throwing two dice − .

(This activity was created by the Shodor Education Foundation)