10.37 Drawing cards. You are about to draw a card at ran- dom (that is, all choices have the same probability) from a set of 7 cards. Although you can't see the cards, here they are: (a) What is the probability that you draw a 9? (b) What is the probability that you draw a red 9? (c) What is the probability that you do not draw a 7.? 10.39 A door prize. A party host gives a door prize to one guest chosen at random. There are 48 men and 42 women at the party. What is the probability that the prize goes to a woman? Explain how you arrived at your answer. 10.41 Living arrangements. (a) Why is this a legitimate nite probability model? (b) What is the probability that the person chosen is a 15 to 19-year-old who lives with others? ((1) What is the probability that the person is 15 to 19 years old? (d) What is the probability that the person chosen lives with others? 10.42 Living arrangements, continued. (a) List the outcomes that make up the event A = {The person chosen is either 15 to 19 years old 01' lives with others, or both} (b) What is P(A)? Explain carefully why P(A} is not the sum of the probabilities you found in parts (b) and (c) of the previous exercise. 10.35 Foreign-language study. Choose a student in a U.S. public high school at random and ask if he or she is studying a language other than English. Here is the distribu- tion of results: Language Spanish French German All others None Probability 0.30 0.08 0.02 0.03 0.57 (a) Explain why this is a legitimate probability model. (b) What is the probability that a randomly chosen student is studying a language other than English? (c) What is the probability that a randomly chosen student is studying French, German, or Spanish