Neat question!
From the prompt, we know that w + b = 8.
S1 tells us that (b / 8) < .2
Since b is a nonnegative integer, we must have either b = 0 or b = 1. In either case, we can't have two black socks at all, so the probability of selecting two black socks = 0.
S2 tells us that (w / 8) > .8
Since w is a positive integer, we must have w = 7 or w = 8. (If w = 6, we'd only have .75, which is too small). As above, this means we can only have 0 or 1 black socks, so picking two of them is impossible and has probability 0.
From the prompt, we know that w + b = 8.
S1 tells us that (b / 8) < .2
Since b is a nonnegative integer, we must have either b = 0 or b = 1. In either case, we can't have two black socks at all, so the probability of selecting two black socks = 0.
S2 tells us that (w / 8) > .8
Since w is a positive integer, we must have w = 7 or w = 8. (If w = 6, we'd only have .75, which is too small). As above, this means we can only have 0 or 1 black socks, so picking two of them is impossible and has probability 0.
