The table below shows the results of a survey of 200 students on their preference for two subjects, Mathematics (M) and English (E). | | Likes M | Does not like M | Total | |---|---|---|---| | Likes E | 60 | 50 | 110 | | Does not like E | 70 | 20 | 90 | | Total | 130 | 70 | 200 | (a) A student is chosen at random from the group. Find the probability that the student: (i) likes both Mathematics and English (ii) likes Mathematics but not English (iii) likes neither Mathematics nor English (b) Given that a student likes Mathematics, find the probability that the student also likes English. (c) Two students are chosen at random without replacement from those who like English. Find the probability that both students like Mathematics. (d) Determine, showing all working clearly, whether the events 'likes Mathematics' and 'likes English' are independent.