Question 1 A group of 200 randomly selected CEOs was tested for personality type. The following table gives the results of this survey. Type Aype Botal Men 84 63 147 Women6 27 53 Total 110 90 200 a) If one CEO is selected at random from this group, find the probability that this CEO Is a woman ii) Is a man given that he has a type A personality iii) Has a type A personality and is a woman iv) Is a man or has a type B personality b) Are the events "woman" and "type A personality" mutually exclusive? Are they independent? Why or why not? Explain.