Answer:
B. 0.27
Step-by-step explanation:
We have these following probabilities:
A 3% probability you will consider someone with high potential.
A 97% probability that you consider someone who does not have high potential.
If a person has high potential, there is a 60% probability that she has an Ivy League degree.
If a person does not have high potential, there is a 5% probability that she has an Ivy League degree.
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
![P = \frac{P(B).P(A/B)}{P(A)}](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7BP%28B%29.P%28A%2FB%29%7D%7BP%28A%29%7D)
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
In this problem, we have that:
What is the probability that a person has high potential, given that they have a Ivy League degree?
P(B) is the probability that a person has high potential. So P(B) = 0.03.
P(A/B) is the probability that a person has an Ivy League degree, given that she has high potential. So P(A/B) = 0.6.
P(A) is the probability that a person has an Ivy League degree. It is 0.6 of 0.03 and 0.05 of 0.97. So
![P(A) = 0.6*0.03 + 0.05*0.97 = 0.0665](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.6%2A0.03%20%2B%200.05%2A0.97%20%3D%200.0665)
What is the probability that they are a high potential?
![P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.03*0.6}{0.0665} = 0.27](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7BP%28B%29.P%28A%2FB%29%7D%7BP%28A%29%7D%20%3D%20%5Cfrac%7B0.03%2A0.6%7D%7B0.0665%7D%20%3D%200.27)
The correct answer is:
B. 0.27