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 accountants ha

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Mathematics

Alice Hayden

7 August, 14:27

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 accountants ha

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Carson Holland · Answer 1

0.3

Step-by-step explanation:

While, this can be easily represented in a Venn Diagram, I'll try to explain it in words to better understand the concept.

From the question, it was stated that

Proportion of accountants with MBA and 5 and above number of years of experience = 0.75 * (proportion of accountants with no MBA degree and less than 5 years of professional experience.

If we say, let X represent the the proportion of accountants with no MBA and less than 5 years of experience,

then the proportion of accountants with MBA degrees and at least 5 years of professional experience = 0.75X

From the question, we are told that accountants with MBA degrees = 35% or 0.35

Hence proportion of people in the firm with an MBA and less than 5 years of experience = 0.35 - 0.75X

We are also told that 45% of the people have less than 5 years of professional experience = 0.45

This means that we can have the number of people with more than 5 years of professional experience as 1 - 0.45 = 0.55

Hence proportion of people having more than 5 years of experience, but no MBA = 0.55 - 0.75X

We then add them up, with the knowledge that addition of all probabilities equals 1

Thus:

X + 0.75X + (0.55 - 0.75X) + (0.35 - 0.75X) = 1

X = 0.40

Then we substitute the value of X into the two established equations, we get:

People who have more than 5 years experience = 0.55 - 0.75 (0.40) = 0.25

People who have only MBA = 0.35 - 0.75 (0.40) = 0.05

Since we want the probability of accountants with MBA degrees or at least 5 years experience, but not both, we add the two probabilities, since "OR" denotes addition in the world of probability

Hence this probability will be equal to 0.25 + 0.05 = 0.3