7. Possessing a boat and renting an apartment are: A. independent events B. mutually exclusive C. both independent and mutually exclusive D. neither independent nor mutually exclusive
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- II. Determine whether the events are mutually exclusive, non-mutually exclusive, independent, or dependent events. 1) A rental agency has 12 white cars, 8 gray cars, 6 red cars, and 3 green cars for rent. Mr. Durant rents a car, returns it because the radio is broken, and gets another car. What is the probability that Mr. Durant is given a green car and then a gray car? 2) A fair die is tossed once and a letter is chosen from the word STATISTIC at random. Find the probability that the number obtained is greater than 1 and the letter obtained is A. 3) A bag contains 4 blue and 8 red balls. If two balls are drawn at random from the bag without replacement, what is the probability that one ball is blue and the other is red? 4) A box of chocolates contains 10 milk chocolates, 8 dark chocolates, and 6 white chocolates. Juanico randomly chooses a chocolate, eats it, and then randomly chooses another chocolate. What is the probability that Juanico chose a milk chocolate, and then, a white…Which of the following pair of events are independent? A) Event I: You sleep late.Event II: You are late for class. B) Event I: You write proper thank-you notes.Event II: You get invited back.C) Event I: The first time you flip a coin, you get head.Event II: The second time you flip a coin, you get tail. D) Event I: General Electric stock goes up.Event II: General Motors stocks goes up.4.)Car Dealership General Motors Toyota Total Car 55 30 85 SUV 28 17 45 Total 83 47 130 If one person selects a vehicle at random from the dealership, determine the probability thát thế person selects a.) а car b.) a vehicle manufactured by General Motors c.) a car manufactured by General Motors
- 4b) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible simple events can be represented as follows: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on board. The events A and B are defined as follows: A= event that Betty and Allison are both selected B = event that Charlie and Dave are both selected Then the events A and B mutually exclusive. True 2 False theIf event (A) is receiving a bachelor’s degree and event (B) is receiving a PhD then events A and B are necessarily: a. None of the above b. Mutually exclusive c. Independent d. ExhaustiveA set of 345 college players (graduates and undergraduates) are interviewed by the NFL to play professional football, 240 players graduated from college, of these 190 studied a major in the humanities (history, philosophy, political science, etc.), a total of 95 players (graduates and non-graduates) studied a specialty in applied sciences (administration, engineering, accounting, etc.) of which 45 did not obtain a degree. The following events are defined: Event A -> Humanities Major Player Event A’ -> Player majoring in science Event B -> Graduated Player Event B’ -> Player not graduated Answer the following questions: What is the probability of interviewing a player with a major in the humanities? What is the probability of interviewing a graduate player with a major in the humanities? If a player majoring in the humanities is interviewed, what is the probability that the player has graduated? What is the probability of interviewing a graduated player? What to…