1. ECON 103 Tutorial 15 Rob Pryce www.robpryce.co.uk/teaching

2. 4.3.5 In an internet café, one of the five PCs is out of order. Two customers arrive; each sits down at a PC. Calculate the probability that: (a) both customers select PCs that are working (b) only one selects a PC that is working (c) both select PCs that are out of order

3. 4.3.11 A box contains 20 hand-held torches, four of which are defective. If 4 torches are selected at random, what is the probability that… (a) no defective torches are selected? (b) two defective torches are selected?

4. 4.4.7 Registration records for five disciplines in a college give the numbers of male and female students as summarised in the table below. (a) For each of the disciplines given, calculate the conditional probabilities that the student is (i) male (ii) female. (b) Calculate the marginal probability distributions for (i) discipline (ii) gender (c) Given that the student is male, calculate the conditional probability distribution that the student is studying each discipline NumbersBusinessEngineeringSciencePharmacyHumanitiesTOTAL Male2144121026050838 Female326881286030632 Total540500230120801470

5. 4.5.5 A retailer buys boxes of pre-packed grapes from three suppliers: 10% from A, 25% from B and 65% from C. Quality control have determined that 90% of packs from supplier A are perfect, while 95% and 82% from B and C are perfect respectively. (a) Calculate the probability that a randomly selected pack of grapes is perfect Supplier Perfect Mouldy Total A B C Total 10,000

6. 4.5.5 A retailer buys boxes of pre-packed grapes from three suppliers: 10% from A, 25% from B and 65% from C. Quality control have determined that 90% of packs from supplier A are perfect, while 95% and 82% from B and C are perfect respectively. (b) A customer returns a mouldy pack of grapes. Calculate the probability that it was supplied by A, B or C.

7. 5.1.7 Part-time hours per week Exam Result01-56-10>10Row Total Distinction301510560 Credit25 102080 Pass35252030110 Fail105 2550 Column Total100705080300 Calculate the joint probability distribution for results and hours worked Calculate the marginal probability distribution for exam results Calculate the marginal probability distribution for hours worked Calculate the conditional probability distribution for results, given that hours worked >10

8. 5.3.3 The roads authority carried out surveys on the volume of traffic on minor roads. On one particular road, an average of 96 vehicles pass a given point between the hours of 3pm and 7pm. A under what conditions would the traffic flow be considered a Poisson process? B calculate the average number of vehicles using the road per hour/minute/15 minutes C calculate the probability that 25 vehicles pass in 1 hour/ 1 vehicle passes in 1 minute.