Expected and Theoretical Probability
# Expected and Theoretical Probability

GCSE(F),

The theoretical probability of an event happening is

probability = `frac(text(number of event outcomes))(text(total of all possible outcomes))`

Use theoretical probability where there is no experiment or survey taking place.

Expected probability can be obtained from the results of a survey. This is **experimental probability**, or **estimated probability**. Estimated probability is

estimated probability = `frac(text(frequency of selected event))(text(total frequency of all events))`

An estimated probability can be used to predict the number of event outcomes:

Predicted number of outcomes = estimated probabilty x total number of outcomes.

## Examples

1. A production line is manufacturing widgets. On one day, there were 34 faulty widgets produced from 5712 widgets manufactured in total. What is the experimental probability of manufacturing a faulty widget?

Answer: `frac(1)(168)`

Estimated probability = `frac(text(frequency of selected event))(text(total frequency of all events))`

`frac(34)(5712)` = `frac(1)(168)`

2. A production ine is manufacturing splidgets. The estimated probability of manufacturing a faulty splidget is 0.033. On one day, the production line manufactured 2066 splidgets. How many would be expected to be faulty?

Answer: 68

Predicted number of outcomes = estimated probability x total number of outcomes

Predicted number of outcomes = 0.033 x 2066 = 68.2 (68 to nearest whole number).

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