The three door quiz show puzzle shows how wrong intuition can be when dealing with probabilities. A contestant in a game show may win a car by choosing which of three doors the car is behind. When you make your guess, the game show host opens one of the two doors you did not choose, […]

## Conditional Probability

Conditional probability questions arise when two possibly linked events,andoccur. We ask, given thathas happened, what is the probability thatwill happen? The equation we use is,the meaning of which is illustrated in the diagram below. What we are in fact doing by saying, ‘given thathas happened’ is excluding the possibility that will not happen. The diagram […]

## Combinations – When Order of Precedence is Taken into Account

We have to pick from a selection of objects, and need to know, in how many ways canobjects be picked from a choice of There are complications. If we are picking in order of preference, then the order of the selection matters. If you are choosing which University to go to, then you will have […]

## Combinations and Permutations – Examples

A choir consists of 13 sopranos, 12 altos, 6 tenors and 7 basses. A group consisting of 10 sopranos, 9 altos, 4 tenors and 4 basses is to be chosen from the choir. a) In how many different ways can the group be chosen? b) In how many ways can the 10 chosen sopranos be […]

## Quartiles and Median From Frequency Tables By Interpolation

We start with the table below which summarises the daily sales in a newspaper shop over a year for the 360 days the shop was open. Sales Number of Days 1 -200 166 201- 400 100 401 – 700 59 701 – 1000 30 1001 -1500 3 To find the lower quartile we use whereare […]

## Coding

Coding is a method of transforming data so that the numbers are easier to manipulate. Numbers that are not too small and not too large are easier to work with, so if the raw data we start with consists of large numbers for example – and finding the standard deviation or variance will make them […]

## Simultaneous Equations Problems Involving the Normal Distribution

Sometimes it happens that we know a population is normally distributed but we don’t have a full set of data and so cannot find the mean and standard deviation from a set of readings. However, given JUST TWO suitable statistics we can find the mean and standard deviation of a list. This is because there […]

## Contingency Tables

A contingency table is a tabular representation of data which falls into several categories. It shows frequencies, or less frequently, probabilities, for particular combinations of values of two qualities or discrete random variables X and Y. Each cell in the table represents a mutually exclusive combination of X-Y values. For example, consider a sample of […]

## Histograms

A histogram is a type bar chart using intervals on the x -axis, with the modification that the interval sizes are not fixed. The frequencies are defined by the areas of the bars, and the y – axis is not a frequency axis, but a frequency density axis. A histogram is better able to represent […]

## More Calculations Involving the Normal Distribution – Finding Probabilities

Suppose we have a distribution We will find using the diagram on the left. This corresponds to a probability of 0.6915 hence Now we will find illustrated by the diagram on the left. Ignoring the minus sign we go to the normal distribution tables and look for the probability corresponding to finding 0.7422. Because we […]