Probability & Statistics Quizzes PDF

Topic: The addition rule, and union vs. intersection Question: Which events are mutually exclusive? Answer choices: A The probability of rolling a sum that’s divisible by 5 and 2 when two dice are thrown. B The probability of drawing a blue gum ball or a pink gum ball from a...

Topic: The addition rule, and union vs. intersection Question: Which events are mutually exclusive? Answer choices: A The probability of rolling a sum that’s divisible by 5 and 2 when two dice are thrown. B The probability of drawing a blue gum ball or a pink gum ball from a jar. C The probability of drawing a black card or an ace from a deck of cards. D The probability of rolling a 10 or a double when a pair of dice is rolled. 127 Solution: B The events in answer choice A are not mutually exclusive, because if you roll a 10, it’s divisible by both 5 and 2, so both events could occur at the same time. The events in answer choice B are mutually exclusive, because you can only draw one gum ball at a time, so you can’t draw a blue gum ball and a pink gum ball at the same time. The events in answer choice C are not mutually exclusive, because if you draw a black ace, you’re drawing a black card and an ace, so both events could occur at the same time. The events in answer choice D are not mutually exclusive, because if you could roll two 5s, your roll is a double and sums to 10, so both events could occur at the same time. 128 Topic: The addition rule, and union vs. intersection Question: Which events are not mutually exclusive? Answer choices: A The probability of drawing an ace and the probability of drawing a king from a deck of cards. B The probability of rolling a sum that is either 8 or 10 when two dice are thrown. C The probability of rolling three 5s in a row when you roll a six-sided die and the probability you roll three 1s in a row when you roll a six- sided die. D The probability of selecting a small dog from an animal shelter and the probability of selecting a brown dog from an animal shelter. 129 Solution: D The events in answer choices A, B, and C are mutually exclusive because they can’t happen at the same time. But the events in answer choice D are not mutually exclusive, because you could choose a small, brown dog, which means you can choose a small dog and a brown dog at the same time. The events can occur at the same time, so they are not mutually exclusive. 130 Topic: The addition rule, and union vs. intersection Question: If we roll one standard 6-sided die, what’s the probability that the outcome is both odd and divisible by 3? Answer choices: 1 A 3 1 B 2 1 C 6 D Can’t be determined 131 Solution: C Let A be the event of rolling an odd number. Then A = {1,3,5} Then let B be the event of rolling a number that’s divisible by 3. Then B = {3,6} The probability that the outcome is both odd and divisible by 3 is the intersection of A and B, which means we need to find any common outcomes in both event spaces. The only overlap is 3, so the intersection is A ∩ B = {3} Then the probability of rolling a 3 is 1 P(A ∩ B) = 6 132