A).4,.4,.2 B).4,.6,.4 C).3,.3,.3 D).5,.3, -.2 E) None of these are legitimate
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1 AP Statistics Probabilities Test Part 1 Name: 1. A randomly selected student is asked to respond to yes, no, or maybe to the question, Do you intend to vote in the next election? The sample space is {yes, no, maybe}. Which of the following represents a legitimate assignment of probabilities for this sample space? A).4,.4,.2 B).4,.6,.4 C).3,.3,.3 D).5,.3, -.2 E) None of these are legitimate 2. If you choose a card at random from a well-shuffled deck of 52 cards, what is the probability that the card chosen is not a heart? A).25 B).50 C).75 D) 1 E) None of these 3. You play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. For any given match you have a probability of.6 of winning. The probability that you win the next two matches is A).16 B).36 C).4 D).6 E) If P(A) =.24 and P(B) =.52 and A and B are independent, what is? 5. If P(A) =.24 and P(B) =.52 and A and B are independent, what is? 6. If P(A) =.24 and P(B) =.52 and A and B are disjoint, what is? 7. If P(A) =.24 and P(B) =.52 and A and B are disjoint, what is? 8. Which of the following events are disjoint (mutually exclusive)? A) Event A = {odd numbers} Event B = {5} B) Event A = {even numbers} Event B = {numbers greater than 10} C) Event A = {numbers less than 5} Event B = {all negative numbers} D) Event A = {the numbers above 100} Event B = {the numbers below -200} E) Event A = {negative numbers} Event B = {odd numbers} 9. Which of the following situations is independent? A) There are two blue socks and a red sock in a drawer. The probability of picking a blue sock and then another blue sock. B) You are playing a game with a deck of cards. The probability of being dealt an Ace and then another Ace? C) You are playing a board game. The probability of rolling a six and then another six? D) Event A = {The probability you studied for a test} Event B = {The probability you did well on the test} The probability you studied and did well on the test. E) You take the SAT two times. The probability that your second score is higher than your first score.
2 10. Which of the following are true? I. A probability must be any number between 0 and 1 inclusive. II. The probability of a union (union means ) of two events is the sum of the probabilities of those events. III. The probability that an event happens is equal to 1 minus the probability that the event does not happen. A) I and II only B) I and III only C) II and III only D) I, II, and III E) None of these sets of answers 11. Government data show that 26% of the civilian labor force has at least 4 years of college and that 15% of the labor force works as machine operators. Can you conclude that because (.26)(.15) =.039, about 4% of the labor force are collegeeducated machine operators? A) Yes, by the multiplication rule B) Yes, by conditional probabilities C) Yes, by the law of large numbers D) No, because the events are not independent E) No, because the events are not mutually exclusive 12. The probability distribution for M&M s is The probability of randomly drawing a blue peanut M&M is Color Probability Brown.3 Red.2 Yellow.2 Green.2 Orange.1 Blue A).1 B).2 C).3 D) 1 E) If,, and, then A).35 B).4 C).65 D).75 E) None of those. The answer is A box contains six red tags numbered 1 though 6, and four white tags numbered 1 through 4. One tag is drawn. Calculate the following probabilities: 14. P(red) 15. P(even number) 16. P(red and even) 17. P(red or even) 18. P(neither red nor even) 19. P(even red) 20. P(red even) 21. P(less than 4 odd) 22. P( the number 5 white) Suppose that for a group of consumers the probability of eating pretzels is.75 and that the probability of drinking Coke is.65. Further suppose that the probability of eating pretzels and drinking Coke is What is the probability of eating pretzels or drinking Coke? 24. What is the probability of eating pretzels assuming that the consumer drinks Coke?
3 25. Based on your answer to question #24 and the given fact that P(pretzels) =.75, is eating pretzels independent of drinking Coke? Explain your answer. Consider the following experiment: The letters in the word AARDVARK are printed on square pieces of tagboard with one letter per card. The eight letters are then placed in a hat and one letter is chosen randomly. 26. Make a probability outcome table for this experiment. (Look at question #12 for an example.) Letter Probability Event V = {the letter is a vowel} Event F = {The letter is in the first half of the alphabet; ie., A M} 27. Assume you pick three letters without replacement. What is the probability they are all vowels? 28. Assume you pick five letters with replacement. What is the probability they are all vowels? 29. Assume you pick five letters with replacement. What is the probability exactly one is a vowel? 30. Assume you pick five letters with replacement. What is the probability at least one is a vowel? Here is the distribution of the age and gender of randomly selected American students: Age Male Female What is the probability that a randomly student is a female? 32. What is the probability that a student is a female given that the student is 35+ years old? 33. What is the probability that a student is either a female or 35+ years old? 34. If four cards are drawn from a standard deck of 52 playing cards and not replaced, find the probability of getting at least one heart. 35. If there are three dice rolled, find the probability of getting triples ie., 1, 1, 1 or 2, 2, 2, or 3, 3, 3 and so on. 36. A coin is tossed 5 times. Find the probability of getting 4 heads. 37. A coin is tossed 5 times. Find the probability of getting at least 1 head.
4 38. The NFC has won the coin toss for the past 12 Super Bowls. (That is actually true.) What is the probability that the NFC will win this year s Super Bowl coin toss? Explain your answer. 39. A zombie takeover has devastated Denton, TX and your neighborhood was one of the first ones hit. A crazed zombie ninja cat crawled into your house, jumped up on your head and sank its teeth into your tasty skull. Great. Now your days are numbered. To make matters worse it s only Monday. And that stupid cat found the breaker box and shut off power to your house with its mad ninja skillz. You rush to your mom s super high tech refrigerated antidote cabinet to find the zombie antidote. You open the latch and peer in but without any light you can t tell which little vial of life saving liquid is which. It s still Monday. *%@^#! you scream. Your mom has told you before in case of this occurrence that there are 3 zombie antidotes, 5 snake bite antidotes, and 4 anti-irs agent antidotes. You only have time to swallow 2 vials before the zombieness overtakes you. What is the probability that you will not die (AKA not turn into a zombified version of yourself)? Bonus: What is wrong with this venn diagram?
5 Here is an article I found the other day. It has a lot of words but is talking about exactly what we are doing now. Read it and pull out the information you need to answer the question at the end. The Probability of Penalizing the Innocent Due to Bad Test Results In modern society two-outcome tests are everywhere. They include drug tests, sobriety tests, disease tests, genetic tests, etc.. The outcome of these tests are either positive or negative, yes or no. We like to think these tests are at least 99% accurate, and yet, horror stories of spurious results seem to abound. Take company-wide drug testing, opponents may claim that at least a third of those identified as drug users will actually be innocent. If we assume the test is 99% accurate, this claim sounds ridiculous. But is it? To analyze the claim we will "grow" a decision tree. Decision trees are a wonderful little device for analyzing anything with two possible outcomes. Every time we reach the end of a branch and have two possibilities we simply create a set of two new branches. For our analysis, we will assume that 2% of all employees actually use drugs. This is lower than the general population but keep in mind that a lot of drug users are unemployed. Also, a company with a clearly stated anti-drug policy will probably have a low proportion of users. The tree's trunk represents the population of all employees. The first set of branches represent the two possible conditions: drug user, not drug user. Next, we add two sets of branches representing the drug test. One set of branches is attached to each of the original two branches. There is a 1% chance of getting a wrong or incorrect result from the test. Finally we add the tree's leaves. Each leaf represents a possible final outcome of the entire process. Note that there are four possibilities. Two of the four possibilities are correct: drug users and drug free individuals are both correctly identified. However, two of the four possibilities are spurious: drug users and drug free individuals are not correctly identified. We are unlikely to hear complaints from a drug user who is incorrectly identified as being drug free. The drug free person identified as a user is another matter. This would be a very upsetting situation. To find the probability of each final outcome as represented by the four leaves simply multiply the probabilities of each branch one must "climb" on the way to reaching the leaf. Note that all the leaf probabilities have to add up to 100%. The percentage of people identified as drug users who are actually innocent can be calculated. Your task: Draw the tree of the above situation. Calculate the
6 probability that if a person fails the drug test they are actually clean.
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