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 number Same as first number 1st throw New number Same as first or second number New number 2nd throw 3rd throw 1 A B B A’ B ’ B’

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 3 of 20 (ii) P(exactly 2 throws|fewer than 4 throws in that turn) = P(exactly 2 throws AND fewer than 4 throws in that turn) P(fewer than 4 throws in that turn) = P(exactly 2 throws ) P(fewer than 4 throws in that turn)= 1 364 8 9  (iii) P(exactly 5 throws in a turn) 6 5 4 3 4 5 6 6 6 6 6 27                  4 SAJC Prelim 9740/2013/02/Q6 A teacher conducted a survey on a large number of students to determine the choice of colours for painting the school hall from 3 colour options of white, green and blue. Of the students surveyed, 40% were boys and 60% were girls. Of the boys, 50% chose white, 20% chose green and the rest chose blue. Of the girls, 25% chose white, 45% chose green and the rest chose blue. Draw a probability tree diagram to illustrate the above information. [1] (i) One student is randomly selected. Find the probability that the student chose white. [1] (ii) Two students are randomly selected. Find the probability that the two students are of the same gender or chose different colours (or both). [3] (iii) Three girls are randomly selected. Find the probability that exactly 1 girl chose white, given that none of them chose blue. [3] [ (i) 0.35 (ii) 1067 1250 (iii) 2744 1215] Solution 0.5 White 0.2 Green Boys 0.3 0.4 Blue 0.6 0.25 White Girls 0.45 Green 0.3 Blue (i) P(student chose white) = 0.4 0.5 0.6 0.25   = 0.35 or 7 20

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 4 of 20 (ii) Required probability = 1 – P(Students are of different gender and chose same colour) = 1 –2 (0.4 0.5 0.6 0.25) (0.4 0.2 0.6 0.45) (0.4 0.3 0.6 0.3)              = 1067 1250 (iii) P(exactly 1 girl chose white | none of the girls chose blue) P(exactly 1 girl chose white and none of the girls chose blue) P(none of the girls chose blue) P(1 out of the 3 girls chose white and the other 2 chose green) P(none of the girls chose blue) )7.0)(7.0)(7.0( )45.0)(45.0)(25.0(1 3C = 2744 1215 5 RI Prelim 9740/02/Q10 The probability that a hockey team wins any match is 1 2 and the probability that it loses any match is 1 6. Three points are awarded for a win, one point for a draw and no point for a defeat. The team plays four matches and the outcome of each match is independent of the other matches. (i) Show that the probability that the team has exactly one draw and exactly one 1defeat is .6 [1] Find the probability that the team (ii) wins the first match and goes on to win exactly one other match, [3] (iii) wins exactly one match, given that it obtains four points. [4] [ (ii)3 16 (iii)9 11] Solution Given P(win) 1 2 and P(defeat) 1 6 1 1 1 P(draw) 12 6 3     (i) P(exactly 1 draw and 1 defeat) = P(1 draw, 1 defeat, 2 wins) 21 1 1 4! 3 6 2 2!        1 6 (shown) (ii) P(wins the first match and goes on to win exactly one other match) 1 2 P(wins one other match and loses or draws in the other 2) 21 1 1 3! 3 2 2 2 2! 16         

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 5 of 20 A B C Y W Y W Y W 0.25 0.35 0.4 0.2 0.3 0.8 0.7 (iii) P(wins exactly one match | obtains four pts) P(wins exactly one match and obtains four points) P(obtains four points) P(1 win, 1 draw, 2 defeats) P(1 win, 1 draw, 2 defeats) P(4 draws)  2 2 4 1 1 1 4! 2 3 6 2! 1 1 1 4! 1 2 3 6 2! 3                    1 9181 1 11 18 81    6 AJC Prelim 9740/2008/02/Q7 modified 3 machines A, B and C produce 25%, 35% and 40% respectively of the golf balls manufactured by a factory. These balls are either yellow or white. Of the balls produced by A and B, 20% and 30% respectively are yellow. It is known that the probability of picking a yellow ball is 0.355. (a) If 3 balls are picked randomly, find the probability that (i) at least 2 are produced by machine B