econ 103 tutorial 15 rob pryce
TRANSCRIPT
4.3.5In 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
4.3.11A 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?
4.4.7Registration 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
Numbers Business Engineering Science Pharmacy Humanities TOTAL
Male 214 412 102 60 50 838
Female 326 88 128 60 30 632
Total 540 500 230 120 80 1470
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
4.5.5A 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.
5.1.7Part-time hours per week
Exam Result 0 1-5 6-10 >10 Row Total
Distinction 30 15 10 5 60
Credit 25 25 10 20 80
Pass 35 25 20 30 110
Fail 10 5 10 25 50
Column Total 100 70 50 80 300
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
5.3.3The 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.