# MTH_245_TEST_2_REVIEW_SOLUTIONS.pdf - 1 Probability must...

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1) Probability must always be between 0 and 1 . The sum of probabilities for all possible outcomes must equal 1 . 2) 2/9 will make all the probabilities add up to 1. 3) 0.23 is okay, 2/5 is okay, 1 is okay, 0 is okay, 3/2 is not okay because it is greater than 1 , 1/15 is okay, 1.43 is not okay because it is greater than 1 , -0.2 is not okay because it is less than 0 , 0.95 is okay 4) a) Taylor tried to use classical probability, but made a mistake because the list of outcomes was not equally likely (some sums are more likely than others because there are more combinations of numbers that add up to that sum) so this answer is not correct. b) Patrick used classical probability (just counting equally likely outcomes) and did it correctly. The probability can be considered the exact answer. c) Riley used empirical probability (doing trials of a probability experiment or collecting data and calculating a relative frequency) and it is correct. The probability is just an approximation. Law of Large Numbers tells us that relative frequencies approach the actual probability as more trials are done. d) Tanya also used empirical probability and it is correct (presuming the programming was correct). The probability is just an approximation. Law of Large Numbers tells us that relative frequencies approach the actual probability as more trials are done. 5) a) Mutually Exclusive ( If we’re rolling the die just once, we can’t roll a 1 and a 3 at the same time .) b) Not (These can both happen; we can both get a one the first time and a three the second time) c) Mutually Exclusive (can’t be under 18 and 21 or older at the same time) d) Not Mutually Exclusive (can own both at the same time) 6) a) Dependent (Whether or not the first apple is green will affect the probability of whether the second apple is red since you are removing an apple from the bag) b) Dependent (Knowing that the temperature outside is below freezing on a randomly selected day will change the probability that the selected day was in the summer) c) Independent (Since the people are randomly selected, their responses shouldn’t affect each other) 7) Not mutually exclusive, Not independent. Not mutually exclusive because the events can happen at the same time: It is possible that the quarterback is injured and out of the game AND the team could still win. Not independent because if the quarterback is injured and out of the game, it changes the probability that the team will win (the probability is less).
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