What’s the probability of drawing a blue, then black sock; what’s the probability of drawing a black sock then blue sock?

Question

Probability of drawing socks from a drawer of 8 black socks, 6 blue & 4 white without replacement .

Answer 1

There are two ways of solving this. Both use the fact that there are 8+6+4=18 socks, with 8 black, 6 blue, and 4 white.

Method 1: the number of ways of drawing a blue, then a black/the number of ways of drawing two socks = 6*8/18*17 = 8/51; a black then a blue will, of course, be the same; if you wish, you may write 8*6/18*17 = 8/51

Method 2, using conditional probability.

There would be 6 blue socks out of 18 for the first sock for a probability of 6/18 = 1/3; then, as 8 black socks remain out of the 17 socks remaining, the probability of picking a black is 8/17

1/3 * 8/17 = 8/51

There would be 8 black socks out of 18 for the first sock for a probability of 8/18 = 4/9; then, as 6 blue socks remain out of the 17 socks remaining, the probability of picking a blue is 6/17

4/9 * 6/17 = 8/51