Write out the sample space and assume each outcome is equally likely. Then give the probability of the requested outcomes. A man is shopping for a new patio umbrella. There is a 10-foot and a 12-foot model, and each is available in black, sky blue, and rust. (a) He buys a 12-foot sky blue umbrella. (b) He buys a 10-foot umbrella. (c) He buys a black-colored umbrella. (a) He buys a 12 foot sky blue umbrella. The probability is $\frac{1}{6}$. (Type an integer or a simpilfied traction) (b) He buys a 10-foot untrella. The probability is (Type an integer or a simpiffect traction)

Step 1 ：The sample space consists of all the possible outcomes. In this case, the man can choose between two sizes (10-foot and 12-foot) and three colors (black, sky blue, and rust). Therefore, the total number of outcomes is 2 * 3 = 6.

Step 2 ：For part (a), there is only one outcome where he buys a 12-foot sky blue umbrella, so the probability is \(\frac{1}{6}\).

Step 3 ：For part (b), there are three outcomes where he buys a 10-foot umbrella (one for each color), so the probability is \(\frac{3}{6} = \frac{1}{2}\).

Step 4 ：For part (c), there are two outcomes where he buys a black-colored umbrella (one for each size), so the probability is \(\frac{2}{6} = \frac{1}{3}\).

Step 5 ：Final Answer: (a) The probability that he buys a 12-foot sky blue umbrella is \(\boxed{\frac{1}{6}}\). (b) The probability that he buys a 10-foot umbrella is \(\boxed{\frac{1}{2}}\). (c) The probability that he buys a black-colored umbrella is \(\boxed{\frac{1}{3}}\).