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Five cards are selected from a 52-card deck for a poker hand. (a) How many simple events are in the sample space? simple events (b) A royal ush is a hand that contains the A, K, Q, J, and 10, all in the same suit. How many ways are there to get a royal flush? ways (c) What is the probability of being dealt a royal flush? (Enter your probability as a fraction.) A university student frequents one of two coffee houses on campus, choosing Tim Hortons 90% of the time and Starbucks 10% of the time. Regardless of where she goes, she buys a decaffeinated coffee on 70% of her visits. (a) The next time she goes into a coffee house on campus, what is the probability that she goes to Tim Hortons and orders a decaffeinated coffee? (Enter your answer to two decimal places.) E (b) Are the two events in part (a) independent? Explain. 0 Yes, because the probability that the student orders a decaffeinated coffee is 0.7 regardless of whether the student visits Tim Hortons or Starbucks. O No, because the probability that the student orders a decaffeinated coffee depends on whether the student visits Tim Hortons or Starbucks. (c) If she goes into a coffee house and orders a decaffeinated coffee, what is the probability that she is at Starbucks? (d) What is the probability that she goes to Tim Hortons or orders a decaffeinated coffee or both? (Enter your answer to two decimal places.)