How To Calculate Probabilities In Kiwi Math

Transcription

1 For Supervisor s Level 1 Mathematics, Determine probabilities Credits: Two 9.30 am Monday 15 November 2010 Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page. You should answer ALL the questions in this booklet. The questions in this paper are NOT in order of difficulty. Attempt all questions or you may not provide enough evidence to achieve the required standard. If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question. 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 Achievement Determine probabilities. Achievement Criteria Achievement with Merit Solve probability problems using theoretical methods. Overall Level of Performance Achievement with Excellence Explore probability situations to solve problems. New Zealand Qualifications Authority, 2010 All rights reserved. No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.

2 2 You are advised to spend 30 minutes answering the questions in this booklet. QUESTION ONE (a) Three different airlines fly from Christchurch to different destinations in New Zealand each week, as shown in the table below. Flights are chosen at random from the table below and awarded to winners of a competition. Airline Number of flights to each destination Auckland Queenstown Mt Cook Rotorua TOTAL FlyNZ Mountain Air Blue Skys TOTAL 140 (i) Anne wins a flight. What is the probability that her flight is to Queenstown? (ii) Jan wins a flight to Auckland. What is the probability that her flight is with FlyNZ?

3 3 (b) NiceFlight airline gives away flights from Wellington as prizes. Three different destinations are available. The probability of flights going to each of the destinations is shown in the table. Destination Probability Greymouth 0.1 Kerikeri 0.4 Queenstown 0.5 John wins two separate prizes with NiceFlight. All flights are chosen at random according to the probabilities in the table. Calculate the probability that John wins flights to two different destinations.

4 4 (c) A cat has four kittens. Assume that each kitten is equally likely to be a female or a male. Explain fully and carefully, by finding and comparing probabilities, which of the following is most likely for the four kittens: There are 4 female kittens. There are 3 female kittens and 1 male kitten. There are equal numbers of female and male kittens.

5 5 QUESTION TWO (a) At a certain garage the probability of a customer buying diesel is ¹ 9. The other customers all buy petrol. ¹ 5 of both diesel and petrol customers pay cash for their fuel. All others pay by credit card. Some of the information is shown on the diagram. cash diesel credit card cash petrol credit card (i) What is the probability that a customer chosen at random bought petrol and paid by credit card? (ii) What is the probability that the next two customers both bought petrol?

6 6 (b) The oil pressure in a vintage car is noted by a warning light. We know that the oil pressure is too low 1% of the time. If the pressure becomes too low, the light should come on. However, the light is not always reliable. When the oil pressure is too low, the light is on 98% of the time. When the oil pressure is okay, the light is on 0.1% of the time. Find the probability that the light is giving an incorrect reading.

7 7 (c) The garage is giving away free cards with each purchase of fuel. Each card comes with one letter on it: W, A, S, or H. W A S H There is an equal chance of the customer being given each letter. When a customer collects all 4 different letters, they can get a free car wash. Describe a probability experiment that a customer could carry out to determine how many purchases, on average, they would have to make to ensure they had got the whole set of 4 different letters. Assume that the customer has access to cards, spinners, dice and random number generators on a calculator or computer. Give sufficient and full detail of the experiment so that someone else could carry out the experiment successfully. Do NOT do the experiment. \

8 8 Extra paper for continuation of answers if required. Clearly number the question. Question number