Respuesta :
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
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
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
[tex]P(A) = 0.6*0.03 + 0.05*0.97 = 0.0665[/tex]
What is the probability that they are a high potential?
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.03*0.6}{0.0665} = 0.27[/tex]
The correct answer is:
B. 0.27
