Fifteen percent of the employees in a company have managerial positions, and 25
ID: 2930863 • Letter: F
Question
Fifteen percent of the employees in a company have managerial positions, and 25 percent of the employees in the company have MBA degrees. Also, 60 percent of the managers have MBA degrees. Using the probability formulas,
(a) Find the proportion of employees who are managers and have MBA degrees. (Round your answer to 2 decimal places.) Proportion of employees=?????
(b) Find the proportion of MBAs who are managers. (Round your answer to 2 decimal places.) Proportion of MBAs =?????
(c) Are the events being a manager and having an MBA independent? No Yes
Explanation / Answer
Here We have given that P(Manager) = 0.15 , P(MBA) = 0.25 and P(MBA | Manger ) = 0.60
(a) Find the proportion of employees who are managers and have MBA degrees ?
That is we have to find P(Manager MBA) .
For any two events A and B, where P(B) 0, you have the conditional probability:
P( A | B ) = P( A B ) / P( B ) = P( B | A) * P(A) / P(B)
So P(Manager MBA) = P(MBA | Manger) * P(Manger)
= 0.60 * 0.15
= 0.09
(b) Find the proportion of MBAs who are managers.
that is we have to find P( Manger | MBA) .
P( Manger | MBA) = P( Manger MBA) / P(MBA)
= 0.09 / 0.25
= 0.36
(c) Are the events being a manager and having an MBA independent?
An event which remains unaffected by previous event or set of events is known as an independent event.
the probability of independent events A and B.
P(A and B) = P(A) * P(B)
P(Manager) = 0.15 , P(MBA) = 0.25 and P(Manager MBA) = 0.09
if events being a manager and having an MBA independent then P(Manager MBA) = P(Manager)* P(MBA)
= 0.15*0.25 = 0.0375
In this way the events being a manager and having an MBA are not independent. So answer is NO.
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