Question

The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 18 restaurants located in a certain city, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to this city 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. (Round your answers to four decimal places.)

(a)

What is the probability that none of the meals will exceed the cost covered by your company?

(b)

What is the probability that one of the meals will exceed the cost covered by your company?

(c)

What is the probability that two of the meals will exceed the cost covered by your company?

(d)

What is the probability that all three of the meals will exceed the cost covered by your company?

Answer 1

total number of restaurants in sample, n = 3

Probability that the meal cost  will exceed $50 ( the amount company does not cover ) = 1/3

Probability that the meal cost  will be below $50 ( the amount company covers) = 1 - 1/3 = 2/3

a) Probability that none of the meals will exceed the cost covered by your company = P[ All three meals below $50 ] = 2/3*2/3*2/3 = 8/27

b) Probability that one of the meals will exceed the cost covered by your company = P[ one meal above $50 and other two below $50 ] = 3*P[ any one meal above $50 ]*P[ any two meals below $50 ] = 3*1/3*2/3*2/3 = 12/27

c) Probability that two of the meals will exceed the cost covered by your company = P[ two meals above $50 and rest below $50 ] = 3*P[ any one meal below $50 ]*P[ any two meals above $50 ] = 3*1/3*1/3*2/3 = 6/27

d) Probability that all three meals will exceed the cost covered by your company = P[ All three meals above $50 ] = 1/3*1/3*1/3 = 1/27