a) In a bag, there are 4 red towels and 3 yellow towels. Towels are drawn at random from the bag, one after the other without replacement, until a red towel is obtained. If X is the total number of towels drawn from the bag, find i. the probability distribution of variable X. (3 mark) ii. the mean of variable X. (2 marks iii. the variance of variable X. (3 marks) b) The probability that a resident of Pearl Island supports political party A is 0.7. A sample of 6 residents of Pearl Island is chosen at random. Find the probability that i. exactly 4 residents support political party A. (3 marks) ii. less than 4 residents support political party A. (4 marks) [15 marks] b) The probability that a resident of Pearl Island supports political party A is 0.7. A sample of 6 residents of Pearl Island is chosen at random. Find the probability that 1. exactly 4 residents support political party A. (3 marks) less than 4 residents support political party A. (4 marks) [15 marks]