RI S2B Binomial Distribution_Tutorial Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _______________________________ Tutorial S2B: Binomial Distribution Page 1 of 3 Tutorial S2B: Binomial Distribution Section A (Discussion Questions) 1 State, with a reason, whether a binomial distribution could be used in each of the following problems. If binomial distribution is an acceptable model, define the random variable clearly and state its parameters. (a) A gambler has a biased coin for which the probability of obtaining a head in any toss is 0.56. Find the probability of getting 6 heads if he tosses the coin 8 times. (b) A fair coin is spun until a head occurs. Find the probability that 8 spins are necessary, including the one on which the head occurs. (c) A jar contains 49 balls numbered 1 to 49. Six of the balls are drawn at random without replacement. Find the probability that four out of the six balls drawn have an even score. 2 Given ~B 1 0 ,0 . 2X , find (i) ; (ii) ; (iii) ; (iv) P(4 8)X ; (v) P(2 6)X ; (vi) E X ; (vii) Var X . [ (i) 0.107 (ii) 0.678 (iii) 0.0328 (iv) 0.121 (v) 0.618 (vi) 2 (vii) 1.6] 3 A die is biased such that the probability of getting a six is 0.18. If the die is thrown ten times, find (i) the probability that the number of sixes that turn up is odd, (ii) the expectation and variance of the number of sixes that turn up. [(i) 0.494, (ii) 1.8, 1.476] 4 Two fair dice are thrown. Find the probability that the total score is two-figured. If five people were each to throw two dice, find the probability that exactly three of them will get a two-figured total score. [ 1 6 , 0.00322] 5 The probability that a patient suffering from a particular disease will be cured following a new treatment is 0.92. (i) If the treatment is given to 10 patients, show that the probability that at least 9 out of the 10 patients will be cured is 0.812, correct to 3 significant figures. (ii) This treatment is being tested at 12 hospi tals where in each hospital, the treatment is given to 10 patients. Find the probabil ity that more than 10 of the 12 hospitals will have a success rate of at least ninety percent. [(ii) 0.310] P( 0)X  P( 2)X  P( 5)X 

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ ________________________________ Tutorial S2B: Binomial Distribution Page 2 of 3 6 According to the school rules, a student who arrives at school after 0730 hours is considered late. (i) During the school term, a boy cycles to sc hool on 5 days each week. On any given day, the probability that he arrives after 0730 hours is 0.1. For a period of 4 weeks, calculate the probability that he is late on at least one day but not more than 3 days. When the boy has cycled to school for the nth time, the probability that he arr