A survey was taken at a firm and the staff were asked if they preferred working from home or at the office. The results of the survey are as follows follow: Work from Home Work at the Office Total Females 90 110 200 Males 75 85 160 165 195 360 The following letters are assigned to the above events: F - Staff is Female M - Staff is Male H - Staff Prefers to Work from Home O - Staff Prefers to Work at the Office a) If a staff is selected at random, what is the probability that they prefer to work at the office? b) If a staff is selected at random, what is the probability that the staff is a female? c) If a staff is selected at random and the selected staff is male, what is the probability that they preferred to work from home? d) If a staff is selected at random and the selected staff is female, what is the probability that they preferred to work from home? e) If a staff is selected at random and the selected staff prefers working from home, what is the probability that the staff is a female? f) If a staff is selected at random and the selected staff prefers working at the office, what is the probability that the staff is a male?

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