Tossing a coin and picking a card

Use this page to introduce the model of joint probabilities underlying contingency table data.

The diagram initially shows a simulation of tossing a coin and picking a card where the joint probabilities are known,

phead, heart  =  phead, club  =  ...  =  ptail, spade  =  1/8  =  0.125

Take a few samples to show the randomness of the sample proportions. Increase the sample size and show that the proportions are less variable.

Select Real data (unknown probabilities) from the pop-up menu at the top. This shows an example where we have sample data in which:

The proportions are estimates of the unknown population joint probabilities.


Travel agents provide 'destination-specific travel literature' about activities, facilities and prices to tourists free of charge on request. A study was made to investigate the differences between information seekers (who requested such literature) and nonseekers, with the aim of better targeting such material.

A sample of 686 tourists was selected and each was classified as an information seeker or non-seeker and in various other ways including educational level.