ACJC H1 LCP1 Question Paper

Name: ______________________________ Tutorial Class: _________________ ANGLO-CHINESE JUNIOR COLLEGE MATHEMATICS DEPARTMENT MATHEMATICS Higher 1 JC2 Learning Checkpoint 1 6th February 2024 25 Marks Time allowed: 45 mins 1 John throws a fair die with faces numbered 1 to 6 and observes the number on the top face of the die. Events A, B and C are defined as follows: A: The score is even. B: The score is divisible by 3. C: The score is not more than 2. State with a reason, which pair(s) of the events if any, are (a) mutually exclusive, [1] (b) independent. [1] 2 In a factory, machines A and B produces drinking mugs. Machine A produces 35% of the mugs and machine B produces 65% of the mugs. 3% of the mugs produced by A are faulty. 6% of the mugs produced by B are faulty. (a) One mug is selected at random. Find the probability that it is faulty. [2] (b) Two mugs are selected at random. (i) Find the probability that exactly one of them is faulty. [2] (ii) Find the probability that exactly one is faulty, given that both were made by A. [2] 3 A group of students are asked whether they own a laptop or a tablet. One of the student is chosen at random. L is the event that the student owns a laptop. T is the event that the student owns a tablet. It is given that P(L) = 2 5 , P(T) = 2 3 and 6P( ) 25LT= . 8865

2 ANGLO-CHINESE JUNIOR COLLEGE 2024 H1 MATHEMATICS 8865/01 (a) Of the students who own a tablet, find the probability that the student also owns a laptop. [2] (b) Find the probability that the student does not own any of these devices. [3] (c) Find the probability that the student owns exactly one of these devices. [2] 4 A librarian arranges 2 Biology books, 3 Chemistry books and 5 Physics books on a shelf. All the books are different. (a) Find the number of different arrangements if the Biology books are placed next to each other. [2] (b) Given that the books are arranged randomly, find the probability that the Chemistry books are not all next to one another. [3] The librarian selects 4 books from the 10 books and the order of selection is unimportant. (c) Find the number of selections if the librarian selects at least one of the Chemistry books. [2] (d) Given that the librarian selects the books at random, find the probability that at most one of the Chemistry books is selected. [3] Summary of Areas for Improvement Knowledge (K) Careless Mistakes (C) Read/Interpret Qn wrongly (R) Presentation (P)