CAIE S1 2016 March — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2016
SessionMarch
TopicConditional Probability
TypeStandard Bayes with discrete events

5 In a certain town, 35\% of the people take a holiday abroad and 65\% take a holiday in their own country. Of those going abroad \(80 \%\) go to the seaside, \(15 \%\) go camping and \(5 \%\) take a city break. Of those taking a holiday in their own country, \(20 \%\) go to the seaside and the rest are divided equally between camping and a city break.
  1. A person is chosen at random. Given that the person chosen goes camping, find the probability that the person goes abroad.
  2. A group of \(n\) people is chosen randomly. The probability of all the people in the group taking a holiday in their own country is less than 0.002 . Find the smallest possible value of \(n\).