So, here is the solution to the problem.
P(X|Y) = P(X∩Y)/P(Y)
P(X∩Y) = P(X) * P(Y|X)
P(X∩Y) = 5000/9000 * 1500/5000 = 15/90
P(Y) = P(X) * P(Y|X) + P(𝑋𝑐) * P(Y|𝑋𝑐)
P(Y) = 15/90 + (4000/9000 * 3000/4000)
P(Y) = 15/90 + 15/90 = 30/90
P(X|Y) = 15/90 * 90/30
P(X|Y) = 15/30 = 1/2