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 .09 (b) find the proportion of mbas who are managers. (round your answer to 2 decimal places.) proportion of mbas 1 (c) are the events being a manager and having an mba independent?

Answer 1

a) 0.09

b) 0.36

c) No

Explanation:

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.

Answer 2

Given

.15 of employees are managers

.25 of employees are MBAs

.60 of managers are MBAs

Find

(a) proportion of employees who are managers with MBA

(b) proportion of MBAs who are managers

(c) whether MBA and manager are independent

Solution

(a) Your answer of 0.60×0.15 = 0.09 is correct

(b) 0.09 of the 0.25 of employees who are MBAs are managers. .09/.25 = 0.36

(c) No. P(MBA | manager) = 0.60 ≠ P(MBA) = 0.25

_____

The only calculation necessary is the one you did for part (a). Other answers can be based directly on the given data. The chart below is unnecessary.