Casino Windsor conducts surveys to determine the opinions 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 1. What proportion of customers rate Casino Windsor as excellent? 2. Determine the probability that a male customer rates Casino Windsor as excellent. 3. Find the probability that a customer who rates Casino Windsor as excellent is a man. 4. Are gender and rating independent? Explain your answer.
| rating | women | men | total |
| excellent | 0.27 | 0.22 | 0.49 |
| good | 0.14 | 0.1 | 0.24 |
| average | 0.06 | 0.12 | 0.18 |
| poor | 0.03 | 0.06 | 0.09 |
| total | 0.5 | 0.5 | 1 |
1)
proportion of customers rate Casino Windsor as excellent =0.49
2)
probability that a male customer rates Casino Windsor as excellent =0.22/0.5=0.44
3)
probability that a customer who rates Casino Windsor as excellent is a man =0.22/0.49
=0.4490
4)
No since P(excellent) =0.49 is not equal to P(excellent |male) =0.44
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