the following questions. Please show all the steps you use to arrive at your answer 1. During a recent survey of ethnic backgrounds of 1000 people in a large city, 513 were Canadian, 148 were French, 72 were African and 56 were Asian and the remainder were from other groups. Calculate the probability that a person, selected at random from the population has: I. a Canadian background? II. an African background? III. an \"other\" background? 6 marks 2. A spinner is divided into three equally sized regions labelled A, B and C. The spinner is spun twice. For each probability you determine, express your answer as a fraction, decimal and percent. I. II. III. IV. What is the probability of spinning A on the first spin? Draw a tree diagram to represent the sample space for both spins. What is the probability of spinning A followed by B? What is the probability of getting the same letter on both spins? 6 marks 3. We have looked in detail at three probability distributions; a) binomial b) geometric c) hypergeometric For each one, I. II. III. Explain the conditions in which we would use it. Justify the formula used. Give an example of a situation in which it could be used. 1. In a library box, there are 8 novels, 8 biographies and 8 war history books. If Jack selects two books at random, what is the probability that the two books are of different types? 3 marks 2. A company manufacturing laptops believes that 5% of their computers are faulty. They take a sample of 30 computers. Showing your calculations, find the probability that; I. II. Two of the laptops are faulty. More than two of the laptops are faulty. 4 marks 3. There are six cats and seven dogs in the local animal shelter. Four animals are chosen at random to visit a local school to educate the children on the great need for homes for these animals. I. II. What is the probability that exactly two of the animals are cats? What is the probability that at least one cat is chosen? 6 marks 4. A certain hockey player scores on 18% of his shots. I. What is the probability he will score for the first time on his fifth shot? II. What is the probability that it will take him fewer than 3 shots to score? III. How many shots should he expect to take before scoring? 6 marks 5. In a multiple choice quiz, there are 6 questions. Each question has 5 possible answers. A student guesses at each question. I. II. III. Find the probability that the student gets 4 answers correct. Find the probability that the student passes (i.e. gets at least 50%) What is the student's expected number of correct answers? 6 marks