Expected and Theoretical Probability

## Expected and Theoretical Probability

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.

## Example 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?

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

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

Answer: frac(1)(168)

## Example 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?

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).