Probability of picking balls out of a box

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events:

values i have discovered that i think are right

A: One of the balls is yellow (1/3)
B: At least one ball is red (3/5)
C: Both balls are green (1/5)
D: Both balls are of the same color (4/15)

P(B|D) = ?

thanks very much

1 yellow, 2 red, 3 green

A: P(no yellow) = 5/6 * 4/5 = 2/3
Hence P(1 yellow) = 1 - 2/3 = 1/3 ... correct

B: P(no red) = 4/6 * 3/5 = 2/5
P(1 or 2 red) = 3/5 ... correct again

C: P(g, g) = 3/6 * 2/5 = 1/5 ... you're on a roll

D: P(g, g or r, r) = 1/5 + P(r, r) = 1/5 + 2/6 * 1/5 = 4/3 * 1/5 = 4/15 ... you're 4 for 4!

P(at least one red | same color) =
P(2 red | same color) = 1/15 / (4/15) = 1/4