Harbourfront House Restaurant (HHR) conducted a survey to find out the busiest mealtime and day for customers. Research participants were asked (i) 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: 39% of participants ate at lunch time. 27% of participants ate at HHR on a weekend. 59.5% of participants ate at IIIIR 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 IIIIR on a weckday? e) Are "weekday" and "lunch time" independent events? Explain mathematically