E
ele
Guest
There are 100 graduates from a high school. Each of them decides, with a constant probability of 0.9 and independently of others, to proceed to university. Suppose that each graduate, among those who decide to enroll in a degree course, enrolls to the Computer Science course with probability 0.75 and independently of others.
Let:
X = "number of graduates that enroll at university"
Y = "graduates that enroll at the Computer Science course".
1) Find p1 = P(X = i), i ∈ [0, ..., 100]
2) Find p2 = P (Y = j), j ∈ [0, ..., 100]
3) Find p3 = P (Y = j | X = i)
4) Find p4 = P (Y = j, X = i)
5) Find p5 = P (X = i|Y = j)
My attempts:
1) For a given i (number of graduates), find the probability of them being enrolled at University: 0.9*i
2) For a given j (number of graduates), find the probability of them being enrolled at the Computer Science university: 0.9*0.75*j = 0.675*j
3) For a given j (number of graduates), find the probability of them being enrolled at computer science university given that i are enrolled at university: Bayes' rule: P(Y|X) = P(X|Y)*P(Y) / P(X) = I can't go on
4) Find probability of the event (there are Y C.S. students ∩ there are X university students): I don't know how to find this
5) Assuming there are j C.S. students, find the probability of having i studentds enrolled at university: P(X|Y) = P(Y|X)*P(X) / P(Y) = same as above
Thanks for the time and the help!
Elle
Let:
X = "number of graduates that enroll at university"
Y = "graduates that enroll at the Computer Science course".
1) Find p1 = P(X = i), i ∈ [0, ..., 100]
2) Find p2 = P (Y = j), j ∈ [0, ..., 100]
3) Find p3 = P (Y = j | X = i)
4) Find p4 = P (Y = j, X = i)
5) Find p5 = P (X = i|Y = j)
My attempts:
1) For a given i (number of graduates), find the probability of them being enrolled at University: 0.9*i
2) For a given j (number of graduates), find the probability of them being enrolled at the Computer Science university: 0.9*0.75*j = 0.675*j
3) For a given j (number of graduates), find the probability of them being enrolled at computer science university given that i are enrolled at university: Bayes' rule: P(Y|X) = P(X|Y)*P(Y) / P(X) = I can't go on
4) Find probability of the event (there are Y C.S. students ∩ there are X university students): I don't know how to find this
5) Assuming there are j C.S. students, find the probability of having i studentds enrolled at university: P(X|Y) = P(Y|X)*P(X) / P(Y) = same as above
Thanks for the time and the help!
Elle