Please help with these 2 probability homework questions



1. A 4-sided balanced die is rolled once and the number of dots X that turned up is observed (X = 1, 2, 3, 4). Then a second balanced 4-sided die is rolled X times. Suppose Y is the total number of dots that turns up after rolling the second die X times:



A. Find Pr( Y=8|X=3 )

B. Find Pr( Y=8 )

C. Find Pr( X=3|Y=8 )





2. A certain discrete random variable X has the following probability mass function (PMF):



P(X=k)= 5 C k • 7 C 3-k / 12 C 3 ; k=0,1,2,3



A. Find Pr(X > 1)

B. Find Pr (X < 1)