question about probability

Question

80% of the inhabitants of Finland are farmers, 2% - are teachers, the rest - other jobs. Find the probability that among the three random selected are:

A - all farmers,

B - 2 farmers and 1 teacher,

C - 2 teachers,

D - at least 1 farmer,

E - all not farmers and not teachers,

F - less than 2 farmers.

Answer 1

P(All Farmers) = (0.8)^3 = 0.512

P(2 Farmers, 1 Teacher) = (0.8)^2 * 0.02 = 0.0128

P(2 Teachers) = (0.02)^2 * 0.98 = .00039

P(At least 1 Farmer) = (0.8)(0.2)^2 + (0.8)^2 * (0.2) + (0.8)^3 = 0.672

P( Not Farmers and Not Teachers) = P(All Other) = (0.18)^3 = 0.0058

P(Less than 2 Farmers) = (0.8)(0.2)^2 + (0.2)^3 = 0.04