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Page 1 of 8 Selwyn College Level 3 Statistics and Modelling 90643 Solve straightforward problems involving probability. Credits: Four Answer ALL questions in the spaces provided in this booklet. You should show ALL working. Check that this booklet has pages 2–8 in the correct order and that none of these pages is blank. YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION. For Assessor’s use only Achievement Criteria Achievement Solve straight forward problems involving probability. Achievement with Merit Solve probability problems. Overall level of Performance Achievement with Excellence Apply probability theory. Page 2 of 8 You are advised to spend 40 minutes answering the questions in this booklet. Show ALL working Question One A biased coin has a 3 chance of landing Heads (H) up. 5 Are you more likely to get one Head or two Heads in three tosses of the coin? Justify your answer. (You may want to draw a probability tree below) Page 3 of 8 Question Two A very large department store sells two types of plasma television. Type A is available 70% of the time and type B is available 85% of the time. Both types are available 65% of the time. A customer wishes to purchase a new plasma television. a) What is the probability that the customer will find at least one type of plasma is available from the department store? b) Are the events “Type A is available” and “Type B is available” independent events? Justify your answer. Page 4 of 8 Question Three The supplier to the department store imports three brands of DVD players. 45% of the DVD players are Brand X, 25% are Brand Y and 30% are Brand Z. It is known that some of the DVD players develop a fault while under warranty. Past experience has shown that 5% of Brand X, 20% of Brand Y and 8% of Brand Z develop a fault while under warranty. a) Find the probability that a randomly chosen DVD player will develop a fault while under warranty. b) Given that a DVD player did develop a fault while under warranty, what is the probability that it was a Brand X DVD player? Page 5 of 8 Question Four The department store is offering an incentive for customers to buy a new DVD player. The customer is given two fair dice to toss. If the sum of the numbers that turn up is 11 or more the customer is given $100 discount on the price of the DVD player. If the sum of the numbers is less than 5 then a discount of $50 is given. If 20 customers buy DVDs during this promotion, find the expected discount on the DVDs. Page 6 of 8 Question Five The movie watching habits of a large number of married couples in the city were analysed. It was found that 15% of husbands watch movies and, if the husband watches a movie then there is a 75% chance the wife also watches the movie. Use this information to calculate the probability that the husband and wife both watch the movie Question Six The department store wants to employ five more sales assistants. Nine females and twelve males apply for the five positions. Calculate the probability that more females than males are appointed to the positions. Page 7 of 8 Question Seven Another large department store has found that 10% of all DVD players purchased in any given year are returned. The manager of the department store is concerned about the number of DVD players which are returned but are not faulty. Data available indicates that 8% of all DVDs are faulty. It is found that 25% of the returned DVDs are in fact not faulty. Calculate the probability that a DVD player that is not faulty is returned. Page 8 of 8