Probability surveys

Probability is often based on surveys, because you get a more accurate measure of probability by basing your calculation on a large number of results.

Newspaper article

Alex is doing some reporting for his local paper. The subject of his article is 'holidays'.

As part of his report he decides to question \(10\) of his friends about whether they prefer caravanning or camping holidays. Seven out of \(10\) say that they prefer caravanning, so Alex writes the headline you can see above.

What is wrong with Alex's method?

Alex has based his probability on a very small survey. This is equivalent to throwing a die \(10\) times, and getting a \(6\) nine times by chance, and then stating that the probability of obtaining a \(6\) is \(\frac{9}{10}\). To estimate probabilities from the results of surveys, you must gather a large number of results.