# Explain the law of large numbers and the central limit theorem. Use an example or analogy to...

## Question:

Explain the law of large numbers and the central limit theorem. Use an example or analogy to illustrate the concept in the simplest terms possible, defining any technical or mathematical terms used.

## Probability theory

It is a branch in statistics and math that deals with analysis of phenomena that are random. This theory expresses concepts as a set or group. For example tossing a coin or throwing dice.

Central limit theorem explains that means of distribution samples are normally distributed as the size of samples become bigger and all the samples in use are similar in size. The shape of population distribution does not matter.

Law of large numbers states that the larger the number of trials, the closer the ratio of outcomes tends to get close to the expected ratio of outcomes. It can also be referred to as the law of averages. It is prone to a gambler?s fallacy which is a type of logical error.

An example is tossing a coin, if a coin is tossed 3000 times the ratio of tails to heads let us say is 1 to 1, if it is then tossed 200 times, there will be a difference in the ratio. 