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

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

In which

P(B|A) is the probability of event B happening, given that A happened.

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

Probability of a scolarship:

15% of 40%(seniors)

30% of 25%(juniors)

20% of 25%(sophmores).

10% of 35%(freshmen). So

Percentage:

0.2727*100 = 27.27%

27.27% of the students with scolarship are seniors.

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step-by-step explanation:

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