10. In this university, among all students, 15% are senior, 25% are junior, 25% are sophomore, and so 35% are freshmen. Among senior, 40% have scholarship; among junior, 30% have scholarship; among sophomore, 20% have scholarship, and among freshmen, 10% have scholarship. Among those have scholoarship, what is the percentage of studens who are senior

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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