Calculating Outcomes

Calculating Outcomes

GCSE(F),

The probabilty of an event occurring is given by:

probability = `frac(text(outcomes))(text(total))`

where outcomes is the number of ways an outcome can occur, and the total is the total of all possible outcomes.

A probability is written as P(event) = value.

The probability of an event NOT happening + the probability of an event happening = 1. As the probability of an event happening plus the probability of an event not happening must add to 1, or

P(not event) = 1 - P(event).

Examples

1. What is the probability of selecting, at random, a red ball from a bag that contains 5 red balls, 7 blue balls, 9 green balls and 9 white balls?

Answer: P(red ball) = `frac(1)(6)`

There are 5 red balls that could be selected.

There are 30 balls altogether.

The probability of selecting a red ball is `frac(5)(30)` = `frac(1)(6)`

2. What is the probability of not throwing a prime number with an eighteen-sided die?

Answer: P(not prime) = `frac(11)(18)`

There are a total of 18 ways of throwing any number.

Prime numbers up to 18 are 2, 3, 5, 7, 11, 13, 17. There are 7 ways of throwing a prime number.

P(prime) = `frac(7)(18)`

P(not prime) = 1 - `frac(7)(18)` = `frac(11)(18)`