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A market research organization has observed that out of 10000 employees, only 200 can stay with the same company for at least 5 years if the candidate has a doctoral qualification. With growing competition worldwide, everyone wants to hire skilled professionals. The executives of a certain financial organization want to decide the expected number of people with a doctoral qualification to stay with their company for next 5 years or more if they hire 30 people.

a) State the probability distribution you use.
b) Write down the probability mass function(p.m.f.) of that distribution. (Remember to put the range of the random variable.)
c) Calculate the expected number of people as required.
d) What is the probability that out of 30 hired professional, less than 5 will continue for 5 years or more?