1.Fifteen people enter a race. How many ways can first, second, and third places be assigned? 2.A bag contains 10 marbles in different colours. If two marbles are drawn, how many different results can be obtained? 3.A deck of 8 cards is dealt to 8 people. How many ways can the cards be assigned? 4.Four dice are rolled. How many different results can be obtained? 5.An exam with 5 questions is given, and students are only required to complete 4 questions. How manyways can the exam be completed?

6. Given P ( A )=0.56, P ( B )=0.34, and P ( A B )=0.2: a. Calculate P ( A |B ). b. Calculate P(B A). c. Are A and B independent? 7. Given P ( A ) =0.64, P ( B )=0.25, and A and B are independent: a. Calculate P( A B). b. Calculate P( AB). c. Calculate P(B A). 8. Four red marbles and eight blue marbles are placed in a bag. Find the probabilities of each outcome: a. Drawing 2 red marbles from the bag without replacing the first marble. b. Drawing 2 red marbles from the bag with replacing the first marble. 9. A poll is conducted prior to an election to see who the favored candidate is among people of different age groups. The following two-way contingency table summarizes the poll results: Age Candidate A Candidate B Undecided 18-30 0.16 0.02 0.02 31-45 0.12 0.10 0.12 46-60 0.08 0.19 0.07 61+ 0.04 0.07 0.01 A random person is selected, find the following probabilities:

10.Are the following random variables discrete or continuous? a.The number of pizzas delivered on a Friday night. b.The amount of gas used to deliver the pizzas. c.The amount of money earned as delivery tips. d.The diameter of the pizzas. e.The number of toppings on each pizza. 11.The following data set is the number of goals scored by a hockey player in a random sample of her games: G={2,0,1,3,1,2,2,1,0,0,3,1,2,0,4,2,1,3,3,1,1,1,0,1,2,0,2,1,1,4,3,0} a.Make a frequency table. b.Calculate the probability of each outcome. c.Graph the probability distribution d.FindP(G1). e.FindP(G<3). f.What is the expected value ofG? g.What is the standard deviation ofG? 12.Chocolate chip cookies are made by placing a scoop of batter onto a cookie sheet to bake. The number of chocolate chips in each cookie is given by the following probability distribution: c0123456 P(c)0.020.080.15u0.290.170.05 a.What is the missing probabilityu? b.How many chocolate chips do most of the cookies have? c.What is the average number of chocolate chips per cookie? d.What is the standard deviation ofC?

13.A student is given a test with only true or false questions. What is the probability the student will pass the test by guessing each answer if the test has: a.5 questions. b.10 questions. c.20 questions. 14.A student is given a test with only multiple choice questions. If each question has 4 options, what is the probability the student will pass the test by guessing each answer if the test has: a.5 questions. b.10 questions. c.20 questions. 15.For each of the following random variables, state whether or not it is a binomial variable and either give thenandpvalues, or explain why it is not a binomial variable. a.The number of females on a team of 5 students selected randomly from a class. b.The number of coins showing heads after tossing 10 coins in the air simultaneously. c.The number of times a die must be rolled to get a six. d.The number of times you draw a card whose suit is hearts from a standard deck of cards when you draw a card, then replace it 7 times. e.The number of questions a student gets right on a test when they answer all questions randomly if the first 10 questions are true or false, and the last 10 questions are multiple choice with 4 options. 16.Calculate the mean and standard deviation of a binomial random variable where: a.n=20,p=0.3 b.n=15,p=0.8 c.n=100,p=0.25 5.GivenXis a binomial random variable, wheren=25,p=0.4, calculate the following probabilities: a.P(5) b.P(X10) c.P(X20) d.P(7X12)