## Seven students, labeled A, B, C, D, E, F, and G, sit in a row of seven seats.

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##### Description

Question 1: Seven students, labeled A, B, C, D, E, F, and G, sit in a row of seven seats.

a) Find the probability that A, B, and C do not sit consecutively (i.e next to each other).

b) Find the probability that B sits on the right-hand side of A. Note, A and B do not need to sit together.

c) If A and B come early and choose two seats next to each other, what is the probability that C and D do not sit together?

Question 2: Consider counting the number of customers to arrive at a Tim Hortons in a given amount of time.

a) Is it reasonable that this counting process follows a Poisson process? Explain by providing a brief explanation on whether or not this process satisfies each of the basic assumptions of a Poisson process.

b) Suppose that customers arrive at a Tim Hortons according to a Poisson process with an average of 20 visits per hour. In the first half hour after opening the store, 15 customers arrive at the Tim Hortons.