A group of 200 randomly selected Chief Executive Officers (CEOS) from Canada were tested for their personality type. The data is shown in the following table: Туре А 102 Туре В 45 Total Men 147 Women 29 24 53 Totals 131 69 200 If one CEO is randomly selected from this group, find the probability that the CEO is: a) Type A personality. b) A man, given Type A personality c) A woman or Type B personality d) Are the events 'man' and Type A personality' independent? Prove mathematically.

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