CASE STUDY CHALLENGE
Probability Distribution: College Admissions
According to an educational board survey, it was observed that class XII students apply at least one to four weeks ahead of college application deadlines. Let \( X \) represent the week when an average student applies ahead of a college’s application deadline.
The probability of the student to get admission in the college \( P(X=x) \) is given as follows:
P(X=x) =
kx/6, when x = 0, 1 or 2
(1-k)x/6, when x = 3
kx/2, when x = 4
0, when x > 4
kx/6, when x = 0, 1 or 2
(1-k)x/6, when x = 3
kx/2, when x = 4
0, when x > 4
Where \( k \) is a real number.
Answer the following:
| (i) | Determine the value of \( k \). | [1 Mark] |
| (ii) | What is the probability that Mahesh will get admission in the college, given that he applied at least 3 weeks ahead of the application deadline? | [1 Mark] |
| (iii) | (a) Calculate the mathematical expectation of the number of weeks taken by a student to apply ahead of a college’s application deadline.
— OR —
(b) To promote early admissions, the college is offering scholarships. Determine the expected scholarship offered by the college using the values: ₹50,000 (4 weeks), ₹20,000 (3 weeks), ₹12,000 (2 weeks), and ₹9,600 (1 week). |
[2 Marks] |