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 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] 6 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 [2] (ii) at least 1 is a yellow ball [2] (iii) at least 1 is yellow given that all the balls picked are from machine A. [2] (b) Due to malfunction of machine A, 10% of the balls produced by machine A is faulty and the event of a ball produced by A is faulty is independent of its colour. Find the proportion of white balls that are faulty and produced by machine A. [3]

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 3 of 7 7 (a) A student threw a fair die four times and recorded the number obtained for each throw. Find the probability that (i) at least two of the four numbers obtained are the same, [2] (ii) exactly two of the four numbers obtained are the same given that the number 6 appeared at least once. [4] (b) Events A and B are such that 1P( ) 2B  , 7P( ) 20A B   and 4P( ) 7B A . Find the probabilityP( )A. [3] 8 (a) Events A and B are such that 1P( ) 3A , 1P( | ) 3B A and 1P( ' ') . 6A B  Find (i) P( )A B , (ii) P( )B . [2][3] (b) A man writes 5 letters, one each to A, B, C, D and E. Each letter is placed in a separate envelope and sealed. He then addresses the envelopes, at random, one each to A, B, C, D and E. (i) Find the probability that the letter to A is in the correct envelope and the letter to B is in an incorrect envelope. [1] (ii) Find the probability that the letter to A is in the correct envelope, given that the letter to B is in an incorrect envelope. [3] (iii) Find the probability that both of the letters to A and B are in incorrect envelopes. [5] 9 A teacher brings 4 black, 3 blue, 2 red and 1 green markers to the classroom for each of his lessons. Unknown to him, the probabilities that a black, blue, red or green marker is out of ink are p,1 2p, 1 4p and 1 8prespectively, where 0 1.p  (i) Find, in terms of p, the probability that a randomly chosen marker from his set of ten markers is out of ink. [2] (ii) In the classroom, the first marker he tries out is out of ink. Find, in terms of p, the probability that the next marker he tries out is a red marker that is also out of ink. [3] (iii) After numerous lessons, the teacher realized that, in general, the first marker he tries out works at least 7 out of 10 times. Find the range of possible values of p. [2]

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ___________________________________________ Additional Practice Questions for Chapter S1B: Probability Page 4 of 7 10 [In this question, give all your answers correct to 3 decimal places.] A delegation of 20 athletes comprises 9 basketball players, 6 volleyball players and 5 tennis players. Among them are 5 male basketball players, 6 male volleyball players and 2 male tennis players. A committee of four people is to be formed from these 20 athletes. (i) Find the probability that exactly three basketball players and one tennis player are chosen. [2] (ii) Find the probability that 2 female athletes are chosen given that at least one volleyball player is chosen. [4] (iii) Determine if the 2 events “2 female athletes are chosen” and “at least one volleyball player is chosen” are independent, justifying your answer. [2] 11 A machine-operated car wash offers four different options as follows: Option Description Duration A Wash only 2 minutes B Wash and dry 3 minutes C Bubble-wash and dry 3 minutes D Steam-wash and dry 4 minutes A driver makes his choice and then proceeds to the car wash. The probability of a driver choosing Option A, Option B, Option C or Option D is given to be 5 12, a, ar and 2ar respectively, where a and r are positiv