Respuesta :
Answer:
0.6154 = 61.54% probability that the student is an undergraduate
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Foreign
Event B: Undergraduate.
There are four times as many undergraduates as graduate students
So 4/5 = 80% are undergraduate students and 1/5 = 20% are graduate students.
Probability the student is foreign:
10% of 80%
25% of 20%. So
[tex]P(A) = 0.1*0.8 + 0.25*0.2 = 0.13[/tex]
Probability that a student is foreign and undergraduate:
10% of 80%. So
[tex]P(A \cap B) = 0.1*0.8 = 0.08[/tex]
What is the probability that the student is an undergraduate?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.08}{0.13} = 0.6154[/tex]
0.6154 = 61.54% probability that the student is an undergraduate
