Answer:
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
