Name: Date: Use the following to answer questions 2-4:

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1 Name: Date: 1. A phenomenon is observed many, many times under identical conditions. The proportion of times a particular event A occurs is recorded. What does this proportion represent? A) The probability of the event A. B) The distribution of the event A. C) The correlation of the event A. D) The variance of the event A. Use the following to answer questions 2-4: A standard deck of cards has 52 cards. The cards have one of 2 colors: 26 cards in the deck are red and 26 are black. The cards have one of 4 denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). 2. One card is selected at random and the denomination is recorded. Which of the following is the correct sample space S for the set of possible outcomes? A) S = {red, black} B) S = {red, red, black, black} C) S = {hearts, diamonds, clubs, spades} D) S = {red, black, hearts, diamonds, clubs, spades 3. Two cards are selected at random and the denomination is recorded. The event H is defined as the event that the first card is hearts. Which of the following correctly defines event H? A) H = {diamonds, clubs, spades} B) H = {hearts, diamonds, clubs, spades} C) H = {(hearts, diamonds), (hearts, clubs), (hearts, spades)} D) H = {(hearts, diamonds), (hearts, clubs), (hearts, spades), (hearts, hearts)} 4. Two cards are selected at random. Event C is defined as the event that the first card is clubs, event R as the event that the first card is red, and event B as the event that the second card is black. Which events are disjoint? A) R and B only. B) R and C only. C) R and B, R and C, but not B and C. D) None of the events are disjoint. Page 1

2 Use the following to answer questions 5-7: If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probabilities for the color of a randomly chosen M&M: Color Brown Red Yellow Green Orange Blue Probability ? What is the probability of drawing a yellow candy? A) 0.1 B) 0.2 C) 0.3 D) Impossible to determine from the information given. 6. What is the probability that you draw neither a brown nor a green candy? A) 0.3 B) 0.6 C) 0.7 D) If you select two M&M's and the colors are independent, then what is the probability that both are the same color? A) 0.01 B) 0.09 C) 0.22 D) 0.25 Page 2

3 8. Suppose a fair coin is flipped twice and the number of heads is counted. Which of the following is a valid probability model for the number of heads observed in two flips? A) B) C) D) None of the above. Use the following to answer questions 9-11: Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to What is the probability that the next three babies are of the same sex? A) B) C) D) Define events A = {the next two babies are boys} and B = {at least one of the next two babies is a boy}. What do we know about events A and B? A) They are disjoint. B) They are complements. C) They are independent. D) None of the above. 11. Define event B = {at least one of the next two babies is a boy}. What is the probability of the complement of event B? A) B) C) D) Page 3

4 Use the following to answer question 12: Consider the following probability histogram for a discrete random variable X: 12. What is P(X 3)? A) 0.10 B) 0.25 C) 0.35 D) The following table describes the probability distribution for the random variable X that counts the number of times a customer visits a grocery store in a 1-week period: Visits or more P(Visits) ? 0.1 The value of the entry in the table for 3 Visits should be: A) 0.2 B) 0.55 C) 0.75 D) 0.25 E) 0.35 Page 4

5 14. Consider the following probability distribution for a discrete random variable X: X P(X = x) What is the P{X 5.5}? A) 0.45 B) 0.75 C) 0.20 D) 0 E) Unable to determine because X is discrete and can't take on the value 5.5. Use the following to answer question 15: Suppose that the random variable X is continuous and takes its values uniformly over the interval from 0 to What is P{X = 1.5 or X = 0.4}? A) 0.75 B) 0.25 C) 0.20 D) 0.80 E) 0 Use the following to answer questions 16-17: Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)} (disregarding order). Let X be the sum of the two balls selected. 16. What is the probability that the sum is at least 4? A) 0 B) 1 3 C) 2 3 D) What is the mean of X? A) 2.0 B) 2.33 C) 4.0 D) 4.33 Page 5

6 Use the following to answer questions 18-20: Let the random variable X be the number of repair calls that an appliance repair shop may receive during an hour. The distribution of X is given below: Value of X Probability What is the value of the missing probability? A) 2 B) 0.2 C) 0.02 D) What is the probability that the repair shop receives at least three repair calls during an hour? A) 0.18 B) 0.2 C) 0.38 D) What is the expected number of repair calls during an hour? A) One call per hour. B) 1.88 calls per hour. C) Two calls per hour. D) More than two calls per hour. 21. Andy has a (toy) garage that is supposed to have four cars in it. According to Andy, X = the number of cars that are actually in the garage at any given time follows the following distribution: Value of X Probability According to this model, what is the average number of cars that are in the garage at any given time? A) 3 cars B) 3.83 cars C) 3.92 cars D) 4 cars Page 6

7 Use the following to answer questions 22-23: Suppose that a college determines the following distribution for X = number of courses taken by a full-time student this semester: Value of X Probability What is the standard deviation of the number of courses full-time students at this college take this semester? A) 0.89 classes B) 0.94 classes C) 1 class D) classes 23. What is P(X > 4.74)? A) 0.25 B) 0.28 C) 0.53 D) Impossible to calculate, because X cannot be Use the following to answer questions 24-27: The weight of medium-size tomatoes selected at random from a bin at the local supermarket is a random variable with mean µ = 10 oz. and standard deviation σ = 1 oz. 24. Suppose we pick four tomatoes from the bin at random and put them in a bag. Define the random variable Y = the weight of the bag containing the four tomatoes. What is the mean of the random variable Y? A) µy = 2.5 oz B) µy = 4 oz. C) µy = 10 oz D) µy = 40 oz Page 7

8 25. Suppose we pick four tomatoes from the bin at random and put them in a bag. Define the random variable Y = the weight of the bag containing the four tomatoes. What is the standard deviation of the random variable Y? A) σy = 0.50 oz B) σy = 1.0 oz C) σy = 2.0 oz D) σy = 4.0 oz 26. Let the random variable W = the weight of the tomatoes in pounds (1 pound = 16 oz). What is the standard deviation of the random variable W? A) σw = 1 16 pound B) σw = 1 pound C) σw = 16 pounds D) σw = 256 pounds 27. Suppose we pick two tomatoes at random from the bin. Let the random variable V = the difference in the weights of the two tomatoes selected (the weight of the first tomato minus the weight of the second tomato). What is the standard deviation of the random variable V? A) σv = 0.00 oz B) σv = 1.00 oz. C) σv = 1.41 oz D) σv = 2.00 oz 28. A random variable X has mean µ = 9 and a standard deviation σ = 2. The random variable X is multiplied by the constant 3 to create a new variable Y, i.e., Y = 3X. What is the variance of Y? A) 36 B) 12 C) 27 D) 6 E) Unable to determine with the information provided. Page 8

9 Answer Key 1. A 2. C 3. D 4. B 5. A 6. B 7. C 8. A 9. B 10. D 11. B 12. D 13. D 14. A 15. E 16. C 17. C 18. B 19. C 20. B 21. B 22. B 23. C 24. D 25. C 26. A 27. C 28. A Page 9