UPSC NDA Math Model Paper 10

Let X be the event that number 4 has appeared at least once and Y be the event that the sum of the numbers appearing is observed to be 5.
i.e X = {(1, 4), (2, 4), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 4), (6, 4)}, Y = {(1, 4), (2, 3), (3, 2), (4, 1)} and X ∩ Y = {(1, 4), (4,1)}
⇒ P (X) = 11/36, P (Y) = 4/36 = 1/9 and P (X ∩ Y) = 2/36 = 1/18
Here we have to find P (X | Y).
As we know that, P(A|B)=

P(A∩B)

P(B)

⇒ P (X | Y) = 1/2