H2MA Remedial _ Probability_Solution (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 (i) ( ) ( ) ( )P P P ' 0.8 0.55 0.25 B A B A B=  −  =− = (ii) Probability that neither A nor B occurs ( ) ( ) P ' ' 1P 1 0.8 0.2 AB AB = = −  =− = (iii) Method 1 ( ) ( ) ( ) ( )( ) P' P P and are independent, and are independent, 1 0.25 0.6 0.45 BC B C B C BC  =  =− = Method 2

Teacher’s copy 2 ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) P' PP P P P and are independent 0.6 0.25 0.6 0.45 BC C B C C B C B C  = −  =− =− = 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 (i) Not defective A Defective Not Defective B Defective Not Defective C Defective (ii) ( )P a sprayer has manufacturing defect 0.65 0.03 0.2 0.04 0.15 0.05 0.035 =  +  +  = ( ) ( ) P 1 out of 2 sprayers has manufacturing defect 2 0.035 1 0.0351 0.06755 =   − = 0.97 0.03 0.65 0.96 0.2 0.04 0.15 0.95 0.05

Teacher’s copy 3 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 (i) P (all counters blue) 6 4 10 4 1 14 C C== (ii) Case 1 : P(3 blue,1 red) 64 31 10 4 8 2