A family consisting of three persons-A, B, and C-goes to a medical clinic that a

Question

A family consisting of three persons-A, B, and C-goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that All three family members are assigned to the same station? (Round your answer to three decimal places.) At most two family members are assigned to the same station? (Round your answer to three decimal places.) Every family member is assigned to a different station? (Round your answer to three decimal places.)

Explanation / Answer

a)

There are 3*3*3 = 27 ways to choose stations.

There are 3 ways to have them at the same station. Hence,

P = 3/27 = 0.111 [ANSWER]

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b)

This is the complement of that in part A, so

P = 1 - 0.111 = 0.889 [ANSWER]

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c)

There are 3! = 6 ways for them to go to 3 different stations. Hence,

P = 6/27 = 0.222 [ANSWER]

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