Dear Tutor, Kindly provide me the answer with explanation, so that i will be more understand. Please show step by step for every calculation. Thank you in advance.

PART A

QUESTION 1 (15 MARKS) a) The probability of Johan taking a bus to work is 0.25. If he takes a bus, the probability of '3) him being late for work is 0.65. If he does not take a bus, the probability of him being late is 0.35. i) Construct a tree diagram for the above information. (4 marks) ii) Find the probability that Johan will not be late for work. (2 marks) iii) Find the probability of Johan taking the bus given that he is late for work. (4 marks) A team consists of 5 members to be formed from 10 students and 5 lecturers. Find the probability that the team will consist of: i) 2 students and 3 lecturers. ii) At least 3 students. QUESTION 3 (1D MARKS) A box contains many pens that are of three colours; green, blue, and red. The probability that a pen is faulty depends on its colour. The probability of a faulty green pen is 0.1, while the probability of faulty blue and red pen is 0.15 and 0.08, respectively. In the box, 35% of the pens are green colour, 40% is blue colour and the rest is red colour. a) Draw a probability tree diagram to represent the above situation. (4 marks) b) Calculate the probability of obtaining a non-faulty pen. (3 marks) 0) If a pen was found to be faulty, what is the probability that it is a green pen? (3 marks) QUESTION 1(20 MARKS) The following data represents the age of Covid-19 patients who have been recorded as fatalities by the Ministryr of Health (MOH) on 6"1 May 2021. 62 79 62 63 73 79 31 44 78 S7 92 79 79 74 62 71 51 57 76 Calculate the following: a) Mean b) Mode c) Median d) variance and the standard deviation (15 marks) e) Obtain the Pearson coefficient of skewness and comment on the distribution