RI 2025 Y6T2W1Mathfocus Probability Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _____________________________________ Y6 H2 Math Term 2 Week 1 Revision: Probability Page 1 of 2 Term 2 Week 1 Revision Topic: Probability 1 The eleven letters in the word CORONAVIRUS are rearranged to form ‘words’ which may not make sense. Find the probability that (i) the two ‘R’s are together; [3] (ii) the vowels (O, A, I, U) are separated; [3] (iii) either the first letter is a ‘C’ or the last letter is an ‘S’ or both. [3] 2 A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. (a) Calculate the probability that (i) all the counters drawn are blue, [1] (ii) at least 3 blue counters are drawn, [2] (iii) at least 1 counter of each colour is drawn, [2] (iv) at least 3 blue counters are drawn, given that at least 1 of each colour is drawn. [2] (b) State with a reason whether or not the events “at least 3 blue counters are drawn” and “at least 1 counter of each colour is drawn” are independent. [1] 3 Camera lenses are made by two companies, A and B. 60% of all lenses are made by A and the remaining 40% by B. 5% of the lenses made by A are faulty. 7% of the lenses made by B are faulty. (i) One lens is selected at random. Find the probability that (a) it is faulty, [2] (b) it was made by A, given that it is faulty. [1] (ii) Two lenses are selected at random. Find the probability that (a) exactly one of them is faulty, [2] (b) both were made by A, given that exactly one is faulty. [3]

Raffles Institution H2 Mathematics 2025 Year 6 _________________________________________________________________________________________ _____________________________________ Y6 H2 Math Term 2 Week 1 Revision: Probability Page 2 of 2 4 For events X and Y, it is given that 1P( ') , 2X Y  3P( ') 4X Y  and 50P( ') . 63X Y  Find (i) P( '),Y [2] (ii) P( ),X [2] (iii) P( ) and state with a reason whether and are independent events.X Y X Y [3]