Question

80% of the employees in a specialized department of a large software firm are computer science graduates. A project team is made up of 9 employees.

Part a) What is the probability to 3 decimal digits that all the project team members are computer science graduates?

Part b) What is the probability to 3 decimal digits that exactly 3 of the project team members are computer science graduates?

Part c) What is the most likely number of computer science graduates among the 9 project team members? Your answer should be an integer. If there are two possible answers, please select the smaller of the two integers.

Part d) There are 43 such projects running at the same time and each project team consists of 9 employees as described. On how many of the 43 project teams do you expect there to be exactly 3 computer science graduates? Give your answer to 1 decimal place.

Part e) I meet 50 employees at random. What is the probability that the third employee I meet is the first one who is a computer science graduate? Give your answer to 3 decimal places.

Part f) I meet 49 employees at random on a daily basis. What is the mean number of computer science graduates among the 49 that I meet? Give your answer to one decimal place.

Answer 1

Let X denote the actual number of Computer Science graduates

probability of success (p) = 0.80

(a)

P(X=9) = ⁹C₉p⁹(1-p)^9-9 = 1*0.8⁹*0.2^(9-9) = 0.134

(b)

P(X=3) = ⁹C₃p³(1-p)^9-3 = 84*0.8³*0.2⁶ = 0.00275

(c)

E(X) = n*p = 9*0.8 = 7.2

the two possible integers are 7 and 8, we choose the answer as minimum value= 7

(d)

In this case probability of success is (p) = 0.00275 and n = 43

Hence,

expected number of projects = n*p = 43*0.00275 = 0.11825

we are allowed to solve four sub parts of a question only.thank you