1) In a group of 400 college students, 154 major in physics, 85 major in history, and 161 major in business. None of these students majors in more than one subject. a) What is the probability that a student chosen at random majors in history? (5 points) b) What is the probability that a student doesn't major in business ? (5 points) (2 points) 2) You are on a game show. You get asked a complicated probability question. The problem is so complicated that you have trouble calculating the correct answer. However, the host tells you it is one of the following answers: -0.3, 0.25, 1.6, and 2.8. You look at the choices and realize what the correct answer must be. draw a) What is the correct answer? (3 points) b) How did you know it was the correct answer? (3 points) b) Are the events in pa joint)? (2 points) 3a) You roll two dice. What is the probability that you roll an odd number on the first die and a 2 on the second die? (5 points) b) Are the events in part a independent or dependent? (2 points)REFERENCE: DECK OF CARDS A standard deck of 52 cards has 4 suits including spades (black), hearts (red), diamonds (red) and clubs (black). Each suit has an ace, a king, a queen, a jack, a ten, a nine, an eight, a seven, a six, a five, a four, a three, and a two (13 cards per suit). The entire deck has 4 of each number (4 aces, 4 kings, 4 twos, 4 threes, etc.) 4a) You draw two cards from a standard deck of 52 without replacing the cards. What is the probability that you will draw a jack on the first card and a jack on the second card? (5 points) living poison ivy. Oil from b) Are the events in part a independent or dependent? (2 points) to go ed off 5 mini 1 10 minutes after the oil washed after 10 min N for strong reaction." The data is below had after 10 minutes () 5a) Given a deck of 52 cards, you pick one card. What is the probability that you will draw either an ace or a club? (5 points) 500 1000 Find the follow (b) P(8 given A) C) P(N and B) d) P(A given N) b) Are the events in part a mutually exclusive (disjoint)? (2 points) 3) A company is offering gift baskets, Lech basket contains one of & favors Wally tones poverty, or strewest), one type of 5 maces pancake init, combreed met on(Log) Bug cinpe (pleck) Esop enif use su ses' s kua sensed alsojc stew's under our 6a) Given a box with 30 blue poker chips, 75 red poker chips, and 60 black poker chips, what is the probability of drawing either a blue chip or a black chip? (5 points) b) Are the events in part a mutually exclusive (disjoint)? (2 points) 7) A random sample of 1000 people participated in a study involving poison ivy. Oil from poison ivy plants was rubbed onto each person's skin. (The people agreed to go through with this. They were paid well.) For 500 of the people, the oil was washed off 5 minutes after being applied. For the other 500 people, the oil was washed 10 minutes after the oil was applied. Let A stand for "washed after 5 minutes," B for "washed after 10 minutes," N for "no reaction", M for "mild reaction," and S for "strong reaction." The data is below: Reaction washed after 5 minutes (A) washed after 10 minutes (B) total none (N) 420 50 ison will be an 470 mild (M) 60 330 rge of quality co 390 strong (S) 20 120 140 total 500 500 1000 Find the following: (16 points) a) P(M) b) P(S given A) c) P(N and B) d) P(A given N) 8) A company is offering gift baskets. Each basket contains one of 3 flavors of jelly (grape, rasberry, or strawberry), one type of 5 mixes (pancake mix, corn bread mix, chocolate cake mix, pudding mix, or stuffing mix), and one of 4 types of sauces (barbecue sauce, marinara sauce, teriyaki sauce, or alfredo sauce). How many ways can a gift basket be put together? (5 points)9) From a group of 11 people, four will be chosen to go to work the late shift. How many ways can the set of three people be chosen? (Remember to consider whether we are dealing with permutations or combinations.) (5 points) 10) From a group of 12 equally qualified people applying for a job at COE SUPERIOR INDUSTRIES, three will be chosen at random to fill three positions. The first person chosen will be the new marketing manager. The second person chosen will be an advisor for the president of the company. The third person chosen will be in charge of quality control. How many ways can the jobs be distributed? (Remember to consider whether we are dealing with permutations or combinations.) (5 points) 12) Consider another binomial experiment, not the one in problem 11, in which therant Its trials and the probability of success on a single the! but are the mean a end and devisation off (10 pointe)11) Arnold has just been given a multiple choice test with 10 questions. Each question has 4 possible answers. Arnold hasn't been to any of the classes or done any homework and thus has no idea what the correct answer is for any of the questions. So he guesses randomly on each question, not knowing if he guesss correctly or incorrectly. (Hint: Consider whether or not this is a binomial experiment.) a) What is the probability that he will answer exactly 6 questions correctly? Round your answer to at least 2 decimal places. (5 points) b) Suppose you want to know the probability that he will answer no more than 6 questions correctly. Write down what you need to do to get the answer without actually calculating it. For example, suppose you needed to find P(5), P(6), P(7), and P(8). Then, without calculating each one, you could just write down the symbols P(5), P(6), P(7), and P(8). indicating whether they should be added, multiplied, subtracted, or divided. If instead you needed P(2), P(3), and P(4), you could write down P(2), P(3), and P(4) and indicating whether they shouldbe multiplied together, added together, subtracted, or divided, without actually calclating the numbers. (5 points) 12) Consider another binomial experiment, not the one in problem 11, in which there are 10 trials and the probability of success on a single trial is p = 0.7. What are the mean u and the standard devisation o? (10 points)