1) Fill in the blanks
a. Probability must always be between _______ and _______. b. The sum of probabilities for all possible outcomes must equal _________ . 2) Fill in the empty spot on this probability model. Outcome Red Blue Green Yellow Purple Probability 191919493) Which of the following numbers could be a probability and which numbers couldn’t?0.23, 2/5, 1, 0, 3/2, 1/15, 1.43, -0.2, 4)We want to find the probability that if we roll two dice, the sum of the numbers on the dice is 9. Four students use different methods to find the probability. Did they use classical or empirical method? Is the method valid or did they make a mistake? Is the probability exact or an approximation? 0.95 b)
Patrick counts 36 outcomes (6 possibilities for the 1stdie, and 6 possibilities for the 2nddie) and counts that four of those outcomes (3&6, 6&3, 4&5, 5&4) would add up to 9, so the probability is 4/36 = 0.1111. c)Riley rolls two dice 1000 times and then counts that there were 106 times that the dice added up to a sum of 9, so the probability is 106/1000 = 0.106 . d)Tanya writes a computer program that simulates rolling two dice 10,000 times. The computer counts that of the 10,000 simulated rolls, 1098 of them added up to a sum of 9 so that probability is 1098/10000 = 0.1098 . 5)Identify if the events E and F are mutually exclusivea) You roll a single die just once.E is “rolling a one”and F is “rolling a three.” ___________b) E is “being under 18 years old”and F is “being 21 years old or older”. ___________ c) E is “owning a PlayStation”and F is “owning an Xbox”. ___________ 6) Identify if the events A and B are independent.a) A bag of apples contains 4 green apples and 6 red apples. You pick two apples without replacement. A is “The first apple you select is green”and B is “The second apple you select is red”. _____________ b) A is “The temperature outside is below freezing”, Bis “The season is summer”. ______________c) You randomly sample two people from a large population and ask them a question. A is “The first randomly selected person responds ‘yes’ to the question” and B is the “The second randomly selected person responds ‘yes’ to the question”.