Question

The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving for a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner.

1. What is the probability that none of the meals will exceed the cost covered by your company?
2. What is the probability that one of the meals will exceed the cost covered by your company?
3. What is the probability that two of the meals will exceed the cost covered by your company?
4. What is the probability that all three of the meals will exceed the cost covered by your company?

Answer 1

Solution: Here, the total restaurants are 15 and one-third of these restaurants the cost of the meal will exceed S50. Thatis 15x5 The probability that none of the meals is 5) 10 P none]- 15 10! 0!(5-0) 3!(10-3)! 15! 3 (15-3)! 1x120 455 120 455 = 0.2637 Thus, the probability that none of the meals will exceed the cost covered by your company is 0.2637

The probability that one of the meals is 5 10 1人2 15 5! 10! 1!(5-1)! 2(10-2)! 15! 3!(15-3)! 5×45 455 225 455 0.4945 0.4945

3. The probability that two of the meals is (5 10 2) 1 15 P (two)-- 10! 2(5-2) 1!(10-1)! 15! 3 15-3)! 10x10 455 100 455 - 0.2198 Thus, the probability that two of the meals wl exceed the cost covered by your company is 0.2198

The probability that three of the meals is 5 10 30 P two) 10! 3!5-3)! 0(10-0 15! 31(15-3)! 10x1 455 10 455 -0.0220 Thus, the probability that three of the meals will exceed the cost covered by your company is 0.0220