Berjaya Builders Bhd is a prominent construction company in Malaysia. This compa

Question

Berjaya Builders Bhd is a prominent construction company in Malaysia. This company has 3 trusted Teams, A, B and C to do all their cost estimation for bidding. Team A does the estimation cost for 40% of the jobs bid by the company, 35% of the cost estimation is done by Team B and remaining by Team C. Probability an error occur in the work of Team A is 0.05. Error rate for Team B is 890 and Team C is 5%. The company stand a chance of 80%, winning a bid it participated. They have participated in 250 bidding for the Year 2014 (a) Construct a tree diagram to represent the above scenario. (b) Determine the number of jobs without erro in cost estimation that the company bids successfully in the year 2014 (c) Suppose a bid arrives and serious error occurs in cost estimation. In your opinion, which team would have done the cost estimation? Explain. A Professor at Faculty of Electrical Engineering, National University wishes to schedule an appointment with each of his seven research assistants, four male and three female, to discuss their research work. (a) Calculate the probability that at least one female research assistant is among the first three with Suppose all possible orderings of appointment are equally likely to be selected. whom the professor meets. (b) Suppose the professor has the same seven research assistants the following semester and again schedules appointments without regard to the ordering during the first semester. Evaluate the probability that the orderings of appointment s are different

Explanation / Answer

Q1

Number of bids submitted by the company = 250

Number of bids submitted by the company that are successful = 250 x 0.8 = 200

Number of bids submitted by the company that are successful and estimated by A

= 200 x 0.4 = 80

Number of bids submitted by the company that are successful and estimated by B

= 200 x 0.35

= 70

Number of bids submitted by the company that are successful and estimated by C

= 200 x 0.25

= 50

Expected number of error-free bids submitted by A = 80 x 0.95 = 76

Expected number of error-free bids submitted by B = 70 x 0.92 = 64.4

Expected number of error-free bids submitted by C = 50 x 0.95 = 47.5

Total expected number of error-free bids submitted by the Company

= 76 + 64.4 + 47.5

= 187.9 ANSWER 1

From the computations given above, 12.1 bids are expected to have error, out of which 4 are likely to be submitted by A, 5.6 are likely to be submitted by B, and 2.5 are likely to be submitted by C. Since A has the maximum possibility, it is fair to suggest that Team A had committed the error. ANSWER 2

Q2

7 research assistants can be ordered among themselves in 7! = 5040 ways.

Number of orders in which the first 3 positions are occupied by male assistants

= (4 x 3 x 2 x 4!) = 576

Number of orders in which there is at least one female assistant in the first 3 positions

= 5040 – 576

= 4464

Hence, probability that at least one female assistant occupies one of the first 3 positions

= 4464/5040

= 0.8857 ANSWER 3

Given the ordering of this semester, the chance the ordering of the next semester is the same as this semester’s

= 1/5040.

Hence, the probability the ordering the two semesters are different = 1 – (1/5040)

= 5039/5040

= 0.9998 ANSWER 4

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