Two marbles are selectod randomly five a box containing 5 red, 7 white and 8 thore marbles one after the other withoet replacement. Find the probutility that (a) both are red; (b) one is white and the other is blase, (c) both are of the mane coloer

To calculate the probabilities, we'll first determine the total number of marbles in the box, which is 5 red + 7 white + 8 blue = 20 marbles. (a) The probability that both marbles selected are red is: P(both red) = (5/20) * (4/20) = 1/20. (b) The probability that one is white and the other is blue can be calculated in two ways (either the first is white and the second is blue or vice versa): P(white first, blue second) = (7/20) * (8/20) = 56/400. P(blue first, white second) = (8/20) * (7/20) = 56/400. Total = 56/400 + 56/400 = 112/400 = 7/25. (c) The probability that both are of the same color takes into account the cases for red, white, and blue: P(both red) = 1/20 (calculated earlier), P(both white) = (7/20) * (6/20) = 21/400, P(both blue) = (8/20) * (7/20) = 56/400. So, P(same color) = 1/20 + 21/400 + 56/400 = 20/400 + 21/400 + 56/400 = 97/400. Thus: (a) P(both red) = 1/20, (b) P(one white and one blue) = 7/25, (c) P(both same color) = 97/400.