Probability Question- Stats

Question

a lady has 6 red socks and 8 yellow socks in a drawer unpaired. In the dark , she pulls out 2 socks, one after the other without replacement . What Is the probability that the lady took out 2 socks of different colors? 

Answer 1

Two different colored socks without replacement means she took out red then yellow or yellow then red. A really easy formula to solve this is the hypergeometric distribution formula, which is essentially all of the combinations of yellow she can pick * all the combinations of red she can pick divided by all of the possible combinations she can pick total.

 

P(pick two different colors) = (choose 1 yellow) * (choose 1 red) / (choose any 2 colors from the total set)

6C1 * 8C1 / 14C2

48/91

 

You can check your work by now checking all of the other possibilities and making sure all of their probabilities sum to 1.

 

P(pick 2 red, 0 yellow) = 6C2 * 8C0 / 14C2 = 15/81

 

P(pick 2 yellow, 0 red) = 6C0 * 8C2 / 14C2 = 28/81

 

48/91 + 15/81 + 28/81 = 91/91