Question

It has been found that 35% of the employees who complete a sequence of executive seminars go on to become vice presidents. Assume that 12 graduates of the program are randomly selected. Find the probability that at least two become vice presidents.

Answer 1

Solution:
Given in the question
P(employees who complete a sequence of executive seminars go on to become vice presidents) = 0.35
Number of sample (N)= 12 Graduates
We need to calculate probability that at least two become vice presidents i.e. P(X>=2) = ?
Here we will use binomial probability distribution as all samples are independent to each other. So binomial distribution formula is
P(X=n |N,p) = NCn*(p^n)*((1-p)^(N-))
P(X>=2) = 1- P(X<2) = 1 - P(X=0) - P(X=1) = 1 - 12C0*(0.35)^0*(1-0.35)^(12-0) - 12C1*(0.35)^1*(1-0.35)^(12-1) = 1 - (1*1*0.0057) - (12*0.35*0.0087) = 1 - 0.0057 - 0.0367 = 1 - 0.0424 = 0.9576
So there is 95.76% probability that at least two become vice presidents.