Casino Windsor conducts survey to determine the opinion of its customers. Among other questions, respondents are asked to give their opinion about "Your overall impression of Casino Windsor". The responses are: Excellent, Good, Average, Poor. In addition, the gender of the respondent is noted. After analyzing the results the following table of joint probabilities was produced:
Rating Women Men
Excellent .27 .22
Good .14 .10
Average .06 .12
Poor .03 .06
(i) What proportion of customers rate Casino Windsor as excellent? 0.49
(ii) Determine the probability that a customer is a male and rate Windsor as
excellent. 0.22
(iii) Find the probability that a customer who rates Windsor as excellent is a man. 0.45
(iv) Are gender and rating independent