Question
Bag A contains 3 red, 4 black, 8 blue and 5 yellow balls.
Bag B contains 5 red, 2 black, 4 blue and 3 yellow balls. Find the probability of drawing 2 blue balls and 1 red ball from either of the bag.Solution
Probability of selecting one bag = 1/2
Probability of drawing 2 blue balls and 1 red ball from bag A = ( 8 c 2  x 3 c 1 )/ 20 c 3 = (28 x 3)/1140 = 7/95
Probability of drawing 2 blue balls and 1 red ball from bag B = ( 4 c 2  x 5 c 1 )/ 14 c 3 = (6 x 5)/364 = 15/182
Required probability = ½ x (7/95 + 15/182)
= 7/190 + 15/364 = (1274 + 1425)/34580 = 2699/34580
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