1. A horticulturist is interested in how many different combinations of carnations there are. For sake of example, let's suppose that a carnation can be defined by three morphological and color characteristics, and all are independent of one another (Main Color, Variegation, and Petal Shape). The main colors of the carnation population she is interested in are purple, white, red, and pink. In terms of variegation, carnations can either be a solid color or be variegated (have a second color). In terms of their petal shape, the petals can either be smooth or jagged. As an example, the carnation in the image below is primarily white, is variegated, and has jagged petals.

A. (0.5 points) What are the total number of outcomes.

B. (0.5 points) Let's say the horticulturist has a specimen of each of the outcomes, and she needs to pick one to show her students in class. What is the probability she picks a white flower to show her students?

C. (1 point) Now, let's suppose that the three events we have been looking at so far (color, variegation, and petal shape) are not entirely independent. If the main color is white, the flower can be variegated or solid white. However, if the main color is pink, red, or purple, the flower can only be solid colored. How many outcomes are there now?

D. (0.5 points) Building off part c, what is the new probability that the flower the horticulturist shows her students is white? What is the probability that it is NOT white?

E. (0.5 points) Building off part c, provided that the flower the horticulturist shows her students is white, what is the probability that the flower is variegated? The probability that the flower is variegated and has jagged petals?