A bag contains 5 Blue, 6 Green, 3 Yellow and 4 Red balls. If four balls are selected at random, then what is the probability that there exist at least two red balls ?
Total ways of selecting 4 balls out of 18 = 18C4 = 3060
Out of the 4 balls at least 2 red colour is possible when, there are (2 Red+2 Non-Red) or (3 Red + 1 Non-Red) Or All Four Red
.'. Ways of selecting at least 2 red balls = (4C2 x 14C2) + (4C3 x 14C1) + 4C4 = 546 + 56 + 1 = 603
Hence, required probability = 603/3060 = 67/340
Correct Option 7)