AQA S3 2006 June — Question 3

Exam BoardAQA
ModuleS3 (Statistics 3)
Year2006
SessionJune
TopicConditional Probability
TypeDice/random device selects population

3 Each enquiry received by a business support unit is dealt with by Ewan, Fay or Gaby. The probabilities of them dealing with an enquiry are \(0.2,0.3\) and 0.5 respectively. Of enquiries dealt with by Ewan, 60\% are answered immediately, 25\% are answered later the same day and the remainder are answered at a later date. Of enquiries dealt with by Fay, 75\% are answered immediately, 15\% are answered later the same day and the remainder are answered at a later date. Of enquiries dealt with by Gaby, 90\% are answered immediately and the remainder are answered at a later date.
  1. Determine the probability that an enquiry:
    1. is dealt with by Gaby and answered immediately;
    2. is answered immediately;
    3. is dealt with by Gaby, given that it is answered immediately.
  2. Determine the probability that an enquiry is dealt with by Ewan, given that it is answered later the same day.