Question

A drawer contains 4 different pairs of gloves. Suppose we choose 3 gloves randomly, what is the probability that there is no matching pair?

My work so far:

-The first pick does not matter.

-The second pick has a 1/7 chance of matching the first glove

-The Third pick has a 1/6 chance of matching the first glove and a 1/6 chance of matching the second glove

Is it correct to say that the P(Match) = P(M1 U M2) where Mx = P(Match at pick x)

P(M1) = 1/7

P(M2) = (1/6)+(1/6) = 1/3

P(Match) = P(M1 U M2) = P(M1) + P(M2) = (1/7) + (1/3) = 10/21

Therefore

P(`Match) = 1-P(Match) = 11/21

Answer 1