probability

Question

8 pairs of hand gloves are on a shelf ( each of different colour). Four gloves are selected at random, the probability that there will be at least one pair is?

Answer 1

P(atleast 1 pair) = 1 – P(0 pair)

P(0 pair) is when all gloves drawn are different

1^st glove: 1 (any of 16)

2^nd glove: 14/15 (after 1^st draw, 15 remain, glove identical to 1 is not to be picked)

3^rd glove: 12/14 (after 2^nd draw, 14 remain, gloves identical to 1,2 are not to be picked)

4^th glove: 10/13 (after 3^rd draw, 13 remain, gloves identical to 1,2,3 are not to be picked)

P(0) = 1* (14/15) * (12/14) * (10/13) = 0.6154

P(atleast 1) = 1 – P(0) = 0.3846