RI S1B Probability_Add Prac_Solns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _______________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 1 of 20 Additional Practice Questions for Chapter S1B: Probability (Solutions) 1 CJC Prelim 9740/2011/02/Q6(b) For events A and B, it is given that 5 2)(P and 10 1)(P ,3 2)'(P  BBABA . Find (i) )'(P BA [1] (ii) )(P A [1] (iii) State whether A and B are independent, giving a reason for your answer. [1] [ (i) 2 5 (ii) 1 2 (iii) and are not independentA B ] Solution (i) )(P1 )'(P)'(P B BABA   5 21 )'(P 3 2   BA 5 2)'(P  BA (ii) 1 2 1P( ) P( ) P( ') 10 5 2A A B A B       (iii) 1P( ) 10A B    1 2 1 1P( ) ( ) and are not independent.2 5 5 10 2 1or P ' P( ) and are not independent.3 2 A P B A B A B A A B            2 9233/2003/02/Q25 In the first stage of a computer game, the player chooses, at random, one of 5 icons, only one of which is correct. If the correct icon is chosen then, in the second stage, the player chooses, at random, one of 8 icons, only one of which is correct. If an incorrect icon is chosen in the first stage then, in the second stage, the player chooses, at random, one of 10 icons; only one of which is correct. The events A and B are defined as follows: A: the first icon chosen is correct. B: the second icon chosen is correct. Find (i) P( )A B , (ii) P( )B , (iii) P( )A B , (iv) P( | )A B. [1][3][2][2] [ (i) 1 40 (ii) 21 200 (iii) 7 25 (iv) 5 21]

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 2 of 20 Solution (i)  1 1P 5 8A B          1 40 . (ii)      P = P + P ' B A B A B  1 4 1 21 40 5 10 200          . (iii)        P = P + P PA B A B A B   = 1 21 1 5 200 40  = 7 25. (iv)     PP P A BA B B  1 4021 200  5 21 . 3 9233/J1997/02/Q3 In each turn of a game, a player throws a fair die repeatedly until he obtains a number that has already appeared in that turn; the player must therefore have at least 2 throws but not more than 7 throws. (i) Find the probability that the player has fewer than 4 throws in a turn. (ii) Find the conditional probability that the player has exactly 2 throws in a turn, given that he has fewer than 4 throws in that turn. (iii) Find the probability that the player has exactly 5 throws in a turn. [ (i) 4 9 (ii) 3 8 (iii) 5 27] Solution (i) P(fewer than 4 throws in a turn) =P(exactly 2 throws in a turn)+P(exactly 3 throws in a turn) = 1 5 2 4 6 6 6 9   Any num