Do you mean that A is a random variable that has a binomial distribution with n = 3 and p = 1/6?

Do oyu mean that B is a random variable that has a geometric distribution with p = 1/2?

If so, then:

i) Two options:

1. .

2. From the cdf, .

ii) Pr(A = B) = Pr(A = 1 | B = 1) Pr(B = 1) + Pr(A = 2 | B = 2) Pr(B = 2) + Pr(A = 3 | B = 3) Pr(B = 3)

Assuming A and B are independent:

= Pr(A = 1) Pr(B = 1) + Pr(A = 2) Pr(B = 2) + Pr(A = 3) Pr(B = 3)