The theoretical probability of an event happening is

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

Use theoretical probability where there is no experiment or survey taking place. *Outcome* means the result of the event: obtaining an even number from a dice gives 3 possible event outcomes out of a total of 6 possible outcomes.

Expected probability will be obtained from the results of a survey, or by random selection. This is **experimental probability**, or **estimated probability**. Estimated probability is

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

If expected probability was being used to monitor faulty widgets being produced in a factory, then the *number of selected event* would be the number of faulty widgets produced, and the *total frequency of all events* would be the total number of widgets produced.

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

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

If a factory monitored faulty widgets being produced over 1 hour, it can obtain a value for an estimated probability. It can then use that figure to estimate how many it produces in a week by multiplying it by th enumber of hours worked in a week.

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?

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

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

Answer: `frac(1)(168)`

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?

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).

Answer: 68

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