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Sagot :
Answer:
27.27% of the students with scolarship are seniors.
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: Has scolarship
Event B: Is a senior
15% are senior, and of those, 40% have scolarship. So
[tex]P(A \cap B) = 0.15*0.4 = 0.06[/tex]
Probability of a scolarship:
15% of 40%(seniors)
30% of 25%(juniors)
20% of 25%(sophmores).
10% of 35%(freshmen). So
[tex]P(A) = 0.15*0.4 + 0.3*0.25 + 0.2*0.25 + 0.1*0.35 = 0.22[/tex]
Percentage:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.22} = 0.2727[/tex]
0.2727*100 = 27.27%
27.27% of the students with scolarship are seniors.
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