In a Friday evening, a restaurant at the La Cantera is full with probability 0.9

Question

In a Friday evening, a restaurant at the La Cantera is full with probability 0.95, independant of any other resurtaurant. A new faculty from UTSA decides to give it a try before going home.

a. Let X equal the number of restaurants visited until the poor faculty find a restaurant with an available table, What is the Probability Mass function of X?

b. What is the probability that the firt available table is at the fourth visited restaurant?

In a Friday evening, a restaurant at the La Cantera is full with probability 0.95, independent of any other restaurant. A new faculty from UTSA a. let X equal the number of restaurants visited until the poor faculty b. What is the probability that the first available table is at the fourth decides to give it a try before going home. find a restaurant with an available table, What is the PMF of X? visited restaurant?

Explanation / Answer

a) This will be a geometric distribution. Hence,

PMF of X = P(X = x) = (0.95)*(0.05)(x - 1)

b) P(First available table is at the fourth visited restaurant)

= P(X = 4)

= (0.95)*(0.05)(4 - 1)

= 0.95*0.053

= 0.00011875

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