CAIE S1 2017 November — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2017
SessionNovember
TopicTree Diagrams
TypeFind unknown probability parameter

5 Over a period of time Julian finds that on long-distance flights he flies economy class on \(82 \%\) of flights. On the rest of the flights he flies first class. When he flies economy class, the probability that he gets a good night's sleep is \(x\). When he flies first class, the probability that he gets a good night's sleep is 0.9 .
  1. Draw a fully labelled tree diagram to illustrate this situation. The probability that Julian gets a good night's sleep on a randomly chosen flight is 0.285 .
  2. Find the value of \(x\).
  3. Given that on a particular flight Julian does not get a good night's sleep, find the probability that he is flying economy class.