M1 Probability Questions?

　
P(A) P(B|A) = P(A∩B)
P(B|A) = P(A∩B) / P(A)

(a)
P(exactly two of the students failed the exam)
= C(45,2) C(60,1) / C(105,3)
= 2970/9373

(b)
P(exactly two of the students failed the exam ∩ the two students come from different class)
= [C(15,1) C(17,1) C(60,1) + C(15,1) C(13,1) C(60,1) + C(17,1) C(13,1) C(60,1)] / C(105,3)
= 2013/9373

P(the two students come from different class | exactly two of the students failed the exam)
= (2013/9373) / (2970/9373)
= 61/90