RI S1B Probability_Add Prac_Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _______________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 1 of 7 Additional Practice Questions for Chapter S1B: Probability 1 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] 2 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] 3 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.

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 2 of 7 4 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] 5 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 o