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1. A marketing research company would like to form a new project team after employing a...

1. A marketing research company would like to form a new project team after employing a project manager. The project team will have 2 analysts and 4 fieldwork supervisors who are selected randomly from two existing project teams (team A and B) of this company. Team A has 3 analysts and 8 fieldwork supervisors and team B has 4 analysts and 9 fieldwork supervisors. What is the probability that equal number of analysts and fieldwork supervisors are selected from team A and team B?

2. Every Friday morning QMB Security Ltd. delivers wages from a local bank to each of the 5 firms in a certain area. Having collected the necessary money from the bank, a security van visits the 5 firms in turn but, as a precaution against robbery, the same route is not used on each occasion. Immediately prior to each Friday's delivery, the van driver chooses at random, according to a procedure established by the operations manager, the order in which of the 5 firms will be visited.

i. What is the probability of the van following a particular route (i.e. visiting the firms in a particular order) on any specific occasion?

ii. What is the probability of the van following a different route on each of 4 consecutive weeks?

iii. What is the probability of 2 particular firms, A and B, being visited consecutively?

3. A company considering launching a new product. It estimates the probability of high sales for the product as 0.6 and low sales at 0.4. The company decides to carry out a market survey, which has a probability of 0.8 being correct. If the market survey predicts high sales, the product will be launched. If the product is launched, what is the probability that the product has high sales?

Math   Statistics-And-Probability   
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Answer #1

1. It is given that the project team will have 2 analysts and 4 field work supervisors

We are asked to find the probabilty that equal number of analysts and field workers are selected from both A and B.

I.e ; Probabity of selecting 1 analyst and two field supervisors from team A out of the 3 analysts and 8 field supervisors + probability of selecting 1 analyst and 2 field supervisors from team B out of the 4 analysts and 9 field supervisors = p( selecting 1 analyst from team A)*p(selecting 2 field supervisors from team A)+ p( selecting 1 analyst from team B)* P( selecting 2 field supervisors from team B)

=(1/3)*(2/8)+(1/4)*(2/9)

=(1/12)+(1/18) = 0.0833+0.0556= 0.1389

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