QUESTION 1 (9 MARKS) A bin contains THREE {3} defective and SEVEN (T) non-defective batteries. Suppose TWO (2) batteries are selected at random without replacement. a) Construct a tree diagram. (4 marks} b) What is the probability that NONE is defective? (2 marks} e) What is the probability that at least ONE (1) is defective? (3 marks} QUESTION 2 (9 MARKS) Rifa is interested in buying pre-loved clothes distributed to orphanages and foster homes. She gathers information on the availability of pre-loved clothes for children from four shops. TABLE 1 shows the number of pre-loved clothes for children based on gender. TABLE 1 Shop Boy (B) Girl (G) Total Goodwill (W) 54 37 91 Poshmark (M) 43 36 79 Depop (D) 82 100 182 Tradesy (T) 16 67 83 Total 195 240 435 a) If one clothing is selected at random, find the probability that it is: i. from Goodwill or Depop. (2 marks) ii. for a girl from Tradesy. (2 marks) iii. from Poshmark given that it is for a boy. (2 marks) b) Are the event "Girl" and "Goodwill" dependent? Justify your answer. (3 marks)QUESTION 3 (18 MARKS) a) Let X be the random variable representing the number of accidents in a certain intersection in a week. The probability distribution of X is shown in TABLE 2. TABLE 2 X 1 3 5 7 9 P(X = X) 0.1 M 0.2 0.3 0.15 Referring to TABLE 2, i . find the value of M. (2 marks) ii. present the information in TABLE 2 into a probability distribution graph. (3 marks) iii. find P(4