Question

In a large accounting firm, the proportion of accountants with MBA degrees and at least five years of professional experience is 75% as large as the proportion of accountants with no MBA degree and less than five years of professional experience. Furthermore, 35% of the accountants in this firm have MBA degrees, and 45% have fewer than five years of professional experience. If one of the firm's accountants is selected at random, what is the probability that this accountant has an MBA degree or at least five years of professional experience, but not both

Answer 1

The probability that this accountant has an MBA degree or at least five years of professional experience, but not both is 0.3

Explanation:

From the given study,

Let A be the event that the accountant has an MBA degree

Let B be the event that the accountant has at least 5 years of professional experience.

P(A) = 0.35

`P(A)^C` = 1 - P(A)

`P(A)^C` = 1 - 0.35

`P(A)^C` = 0.65

`P(B)^C` = 0.45

P(B) = 1 -
`P(B)^C`

P(B) = 1 - 0.45

P(B) = 0.55

P(A ∩ B ) = 0.75
`P(A^C \ \cap \ B^C)`

P(A ∩ B ) = 0.75 [ 1 - P(A ∪ B) ] because
`P(A^C \ \cap \ B^C)` =
`P(A \cup B)^C`

SO;

P(A ∩ B ) = 0.75 [ 1 - P(A) - P(B) + P(A ∩ B) ]

P(A ∩ B ) = 0.75 [ 1 - 0.35 - 0.55 + P(A ∩ B) ]

P(A ∩ B ) - 0.75 P(A ∩ B) = 0.75 [1 - 0.35 -0.55 ]

0.25 P(A ∩ B) = 0.075

P(A ∩ B) =
`(0.075)/(0.25)`

P(A ∩ B) = 0.3

The probability that this accountant has an MBA degree or at least five years of professional experience, but not both is: P(A ∪ B ) - P(A ∩ B)

= P(A) + P(B) - 2P( A ∩ B)

= (0.35 + 0.55) - 2(0.3)

= 0.9 - 0.6

= 0.3

∴

The probability that this accountant has an MBA degree or at least five years of professional experience, but not both is 0.3