Answer: 40/81
===========================================
Work Shown:
B = selecting 1 blue
R = selecting 1 red
P(B) = 5/9, since there are 5 blue out of 5+4 = 9 total
P(R) = 4/9, since there are 4 red out of 9 total
P(2 blue) = P(B)*P(B) = (5/9)*(5/9) = 25/81
P(2 red) = P(R)*P(R) = (4/9)*(4/9) = 16/81
The last two equations are valid because we are sampling with replacement. Each selection is independent.
-------------------
P(2 same color) = P(2 blue OR 2 red)
P(2 same color) = P(2 blue) + P(2 red)
P(2 same color) = 25/81 + 16/81
P(2 same color) = (25+16)/81
P(2 same color) = 41/81
-------------------
P(2 different color) = 1 - P(2 same color)
P(2 different color) = 1 - 41/81
P(2 different color) = 81/81 - 41/81
P(2 different color) = (81-41)/81
P(2 different color) = 40/81
