Of the people entering a blood bank to donate blood, 1 in 3 have type O+ blood, and 1 in 15 have type O blood. For the next three people entering the blood bank, let X denote the number with O+ blood and Y the number with O blood. Assuming independence among the people with respect to blood type, find the probability distributions for X and Y. Also find the probability distribution for X +Y, the number of people with type O blood.