H2MA Remedial _ Probability (RVHS)

Teacher’s copy 1 RVHS H2 Mathematics Remedial Programme Topic: Probability Basic Mastery Questions 1. MI Prelim 9758/2021/Q6(i),(ii),(iii) The events A and B are such that ( )P 0.6A = , ( )P 0.8AB= and ( )P ' 0.55AB= . (i) Find the probability that B occurs. [1] (ii) Find the probability that neither A nor B occurs. [1] A third event C is such that B and C are independent and ( )P 0.6C = . (iii) Find ( )P' BC . [2] Answer: (i) 0.25 (ii) 0.2 (iii) 0.45 2. RVHS Prelim 9758/2021/Q8(i),(ii) A manufacturer produces 3 types of spray bottles: Type A , Type B and Type C . 65% of the sprayers manufactured are Type A and 20% are Type B . 3% of Type A sprayers, 4% of Type B sprayers and 5% of Type C sprayers have manufacturing defects. (i) A sprayer is chosen at random. Construct a probability tree to show the above information. [2] (ii) Find the probability that out of 2 randomly selected sprayers, exactly one of them has manufacturing defects. [3] Answer: (ii) 0.06755 3. CJC Prelim 9758/2020/02/Q6(a) A bag contains 4 red counters and 6 blue counters. 4 counters are drawn from the bag at random, without replacement. Calculate the probability that: (i) all the counters drawn are blue, (ii) at least 3 blue counters are drawn, (iii) at least 1 counter of each colour is drawn, (iv) at least 3 blue counters are drawn, given that at least 1 of each colour is drawn. Answer: (i) 1 14 (ii) 19 42 (iii) 97 105 (iv) 40 97

Teacher’s copy 2 4. HCI Prelim 9758/2020/02/Q7(a) A team of 15 students was selected for an outdoor education trip. One student volunteered to be the trip leader while another volunteered as the assistant trip leader. They decided to have some ice-breaker games, where all 15 students sat in a circle. Find the probability that both leaders were not seated together. [2] Answer: 0.857 5. JPJC Prelim 9758/2020/02/Q6(i) The eleven letters in the word CORONAVIRUS are rearranged to form ‘words’ which may not make sense. Find the probability that the two ‘R’s are together; [3] Answer: 0.182

Teacher’s copy 3 Standard Questions 1. RVHS Prelim 9758/2020/02/Q6 A set of 36 cards is made up of cards chosen from a few packs of ordinary playing cards. The breakdown of the number of cards in each suit and denomination is given in the following table. Suit Denomination Spade Heart Diamond Club Ace 1 2 2 1 K