Of the employees in a specialized department of a large software firm are comput
ID: 3239515 • Letter: O
Question
Of the employees in a specialized department of a large software firm are computer science graduates. A project team is made up of 8 employees. What is the probability to 3 decimal digits that all the project team members are computer science graduates? What is the probability to 3 decimal digits that exactly 3 of the project team members are computer science graduates? What is the most likely number of computer science graduates among the 8 project team members? Your answer should be an integer. If there are two possible answers, please select the smaller of the two integers. There are 57 such projects running at the same time and each project team consists of 8 employees as described. On how many of the 57 project teams do you expect there to be exactly 3 computer science graduates? Give your answer to 1 decimal place. meet 50 employees at random. What is the probability that the second employee I meet is the first one who is a computer science graduate? Give your answer to 3 decimal places. meet 82 employees at random on a daily basis. What is the mean number of computer science graduates among the 82 that I meet? Give your answer to one decimal place.Explanation / Answer
Pr (Computer science graduate) = 0.70
Project team composes = 8 employee
(a) Pr( all projec team member are CS graduate) = 8C8 * (0.70)8 = 0.0576
(b) Pr( 3 are CS Graduate) = 8C3 * (0.70)3 (0.3)5 = 0.04667
(c) Most likely number of CS graduates in a project team = 8 * 0.7 = 5.6
so it may be 5 or 6 so lets calculate probability of having 5 or 6 members in a project team
Pr (5 member) = 8C5 * (0.70)5 (0.3)3 = 0.2541
Pr(6 member) = 8C6 * (0.70)6 (0.3)2 = 0.2965
so Answer should be 6 member
(d) There are 57 such project so Expected number of project having 3 CS graduate
Pr( n; 57) = 57 * Pr(3 CS graduate) = 57 * 0.04667 = 2.7
(e) I met 50 employees, that is irrelevant here. But the second employee i met is the first one who is CS graduate
so Probability of that event is = Pr( Not CS graduate) * Pr(CS graduate) = 0.3 * 0.7 = 0.21
(f) Mean number of computer science graduates among the 82 met = 82 * 0.7 = 57.4
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