Prime DSE Series - Mathematics Mock Exam Papers (Extended Part) Module 1 Set 3

HKDSE-MATH-EP(M1)(Set 3) − 14 14 © United Prime Educational Publishing (HK) Ltd. Answers written in the margins will not be marked. Answers written in the margins will not be marked. Answers written in the margins will not be marked. 10. There are 10 diagnostic rooms in a clinic. For each diagnostic rooms, the number of patients received follows a Poisson distribution with a mean of 2.8 per hour. If the number of patients received by a diagnostic room is at least 3 in an hour, the diagnostic room is regarded as busy in that hour. (a) Find the probability that a certain diagnostic room is busy in an hour. (3 marks) (b) Find the probability that no more than 3 diagnostic rooms are busy in an hour. (3 marks) (c) Find the probability that exactly 3 diagnostic rooms are busy in an hour and total number of patients received by these busy diagnostic rooms in that hour is 11. (3 marks) (d) Given that no more than 3 diagnostic rooms are busy in an hour, find the probability that the total number of patients received by these busy diagnostic rooms in that hour is 11. (4 marks) Sample © United Prime Educational Publishing (HK) Limited All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publisher.