Business stat 1- Consider an experiment with three possible outcomes; 1, 2, and 3. (a) What is the sample space for this experiment? (b) Suppose that P(1) = 0.5 and P(2) = 0.1. What is P(3)? (c) Let A = {1, 2}. What is P(A)? 2- Consider a standard deck of 52 cards. You plan to draw a card at random from this deck and observe the suit and rank of the card. Let B represent the event that you obtain a card with a black suit, Q that you obtain a queen, T that you obtain a ten, H that you obtain a heart, and C that you obtain a club. For each of the following pairs of events, indicate whether the events are mutually exclusive, independent, or neither. Explain your reasoning. (a) Q and B (b) Q and T (c) T and H (d) H and C 3.Twenty people each buy a single ticket for a raffle. There are four prizes to be awarded in the raffle, each with a different dollar value. If each person can win at most one prize, then in how many ways can the four people be selected to win a prize? 4.Consider a class containing 30 students. (a) You wish to select a simple random sample of 10 students. How many different samples are possible? You may assume that the order of selection is irrelevant. (b) Of the 30 students in the class, 8 of them have green eyes. If you select a simple random sample of 10 students, what is the probability that exactly 3 of them will have green eyes? Explain your reasoning. 5.An introductory probability course has 100 students who can be divided by gender and soft drink preference (Brand A, Brand B, or other) as described in the following contingency table. Suppose that one of the students in this course is selected at random. What is the probability that the student (a) is female? That is, what is P(F)? (b) prefers Brand B? That is, what is P(B)? (c) is female and prefers Brand B? That is, what is P(F _B)? 7. Consider the group of all people that purchased a car in 2015. Suppose that 78% of these people requested an automatic transmission, 42% requested a satellite radio, and 27% requested both of these features. Let A represent the event that a randomly chosen Business stat person from this group requested an automatic transmission, and R be the event that they requested a satellite radio. NOTE: In parts (A) - (D) you must first express each probability in terms of the events A and R. (a) What is the probability a randomly chosen person in this group requested at least one of these two features? (b) What proportion of the people in this group requested neither feature? (c) What proportion of the people in this group requested an automatic transmission but did not request a satellite radio? (d) If a person in this group requested an automatic transmission, what is the probability that they also requested a satellite radio? 8. Building 8. Building contracts were issued last year to three contractors starting up a new subdivision of houses. Tamarack Homes built 48% of the houses, Ashcroft Homes built 30% of the houses, and Richcraft Homes built the remaining 22% of the houses. Each Tamarack house has a 4% chance of developing a leaky basement in its first year, independent of each other Tamarack house. Houses built by Ashcroft and Richcraft have the same problem 8% and 14% of the time, respectively. Answer the following questions by first defining four appropriate events, and then expressing the required probability in terms of these events. (a) What is the probability that a randomly selected house will develop a leaky basement? (b) One of the homes has developed a leaky basement within the first year. What is the probability that this house was built by Tamarack Homes