22 S2 Probability APQ (RVHS)

H2 Mathematics (9758) River Valley High School, Mathematics Department, 2022 12 Additional Practice Questions 1. [HCI/2007/JC2/CT] Loy is a member of his school’s soccer team, and the team is participating in an invitation tournament where each team is to play a total of 3 matches. The probabilities that Loy gets selected to play in the first match and the second match are and respectively. The probability that Loy gets selected to play in the third match, given that he was selected to play in the second match is ; and the probability that Loy gets selected to play in the third match, given that he was not selected to play in the second match is . Find the probability that (i) Loy is not selected to play in the third match, (ii) Loy gets selected to play in all the 3 matches, (iii) Loy gets selected to play in at most 1 of the 3 matches. [(i)଻ ଵହ (ii) ସ ଶ଻ (iii) ଶଷଷ ଽସହ] Let event S = Loy gets selected to play (i) P(2nd S, 3rd S’) + P(2nd S’, 3rd S’) = (4/7)(2/3) + (3/7)(1/5) = 7/15 (ii) (7/9)(4/7)(1/3) = 4/27 (iii) P(1st S’, 2nd S’, 3rd S’) + P(S, S’, S’) + P(S’, S, S’) + P(S’, S’, S) = (2/9)(3/7)(1/5) + (7/9)(3/7)(1/5) + (2/9)(4/7)(2/3) + (2/9)(3/7)(4/5) = 233/945 7 9 4 7 1 3 4 5 S S’ S S’ S S’ 7/9 4/7 2/9 3/7 4/7 3/7 S S’ S S’ 1/3 2/3 4/5 1/5 S S’ S S’ 1/3 2/3 4/5 1/5 1st match 2nd match 3rd match

H2 Mathematics (9758) River Valley High School, Mathematics Department, 2022 13 2. [ACJC/2010/Prelim/8] A girl is given two toys, a doll and a teddy bear. The probability that she plays with the doll is 0.5 and the probability that she plays with the teddy bear is 0.6. The probability that she plays with the doll or the teddy bear or both is 0.8. Find the probability that (i) She plays with the doll but not the teddy bear. (ii) She plays with the doll given that she does not play with the teddy bear. [(i) 0.2; (ii) 0.5]

H2 Mathematics (9758) River Valley High School, Mathematics Department, 2022 14 3. [RI(JC)/2011/Promo/9] A group of students take a physical fitness test. A student who fails the test on the first attempt is allowed one further attempt. For a randomly chosen student, the probability of passing the test on the first attempt is 0.6 and the probability of passing on the second attempt is 0.8. (i) Draw a tree diagram to represent the possible outcomes. (ii) Find the probability that a randomly chosen student fails the test on both attempts. (iii) Given that a student passes the test, find the probability that it is on the second attempt. (iv) Three students taking the test are chosen at random. Find the probability that two of them pass on the first attempt and the other pa