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Harbourfront House Restaurant (HHR) conducted a survey to nd out the busiest mealtime and day for customers. Research participants were asked (1) whether they ate at HHR on a weekday or on a weekend ( ii) whether they like to eat at HHR during lunch time or dinner time. The survey reported that: o 39% of participants ate at lunch time. I 27% of participants ate at HHR on a weekend. 0 59.5% of participants ate at HHR during dinner time and on a weekday. a) What is the probability that a randomly selected participant ate at HHR during lunch time or ate at HHR on a weekend? b) Are \"weekend\" and \"dinner time\" mutually exclusive events? Explain mathematically. c) What is the probability that a randomly selected participant ate at HHR on a weekday knowing that the participant ate at HHR during lunch time. d) What is the probability that a randomly selected participant ate at HHR during lunch time and ate at HHR on a weekday? e) Are \"weekday\" and \"lunch time\" independent events? Explain mathematically