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 14 -foot model, and each is available in black, sky blue, and rust. (a) He buys a 14 -foot sky blue umbrella. (b) He buys a 10-foot umbrella. (c) He buys a black-colored umbrella. (b) He buys a 10-foot umbrella. The probability is \( \square \). (Type an integer or a simplified fraction.)

First, let's outline the sample space. The man has two models of patio umbrellas (10-foot and 14-foot) and three colors (black, sky blue, rust). Therefore, the complete sample space consists of the following outcomes: 1. 10-foot black 2. 10-foot sky blue 3. 10-foot rust 4. 14-foot black 5. 14-foot sky blue 6. 14-foot rust This results in a total of 6 equally likely outcomes. Now, we can find the probabilities for each requested outcome: (a) The outcome "buys a 14-foot sky blue umbrella" corresponds to 1 favorable outcome out of 6 total outcomes. Thus, the probability is \( \frac{1}{6} \). (b) The outcome "buys a 10-foot umbrella" corresponds to 3 favorable outcomes (10-foot black, sky blue, rust) out of 6 total outcomes. So, the probability is \( \frac{3}{6} = \frac{1}{2} \). (c) The outcome "buys a black-colored umbrella," which can be either 10-foot black or 14-foot black, corresponds to 2 favorable outcomes out of 6. Therefore, the probability is \( \frac{2}{6} = \frac{1}{3} \). The probability for the repeated request (b) remains \( \frac{1}{2} \) as calculated above.