91Ó°ÊÓ

The number of persons in a family is 3; they are, A, B, and C.

They went to a medical clinic that has a doctor at each of stations 1, 2, and 3.

Each member visits the clinic once and is assigned the station number.

The outcome of an experiment (1,2,1) for A to station 1, B to station 2, and C to station 1.

a.

Let S represents the sample space.

The sample space for the given experiment is,

\(S = \left\{ \begin{aligned}\left( {1,1,1} \right),\left( {1,1,2} \right),\left( {1,1,3} \right),\left( {1,2,1} \right),\left( {1,2,2} \right),\left( {1,2,3} \right),\left( {1,3,1} \right),\left( {1,3,2} \right),\left( {1,3,3} \right),\left( {2,1,1} \right),\left( {2,1,2} \right),\\\left( {2,1,3} \right),\left( {2,2,1} \right),\left( {2,2,2} \right),\left( {2,2,3} \right),\left( {2,3,1} \right),\left( {2,3,2} \right),\left( {2,3,3} \right),\left( {3,1,1} \right),\left( {3,1,2} \right),\left( {3,1,3} \right),\left( {3,2,1} \right)\\\left( {3,2,2} \right),\left( {3,3,1} \right),\left( {3,3,2} \right),\left( {3,3,3} \right)\end{aligned} \right\}\)

b.

Let A represents the event that all three members go to the same station.

The possible numbers of outcomes are,

\(A = \left\{ {\left( {111} \right),\left( {222} \right),\left( {333} \right)} \right\}\)

c.

Let B represents the event that all members go to different stations.

The possible outcomes of event B is represented as,

\(B = \left\{ {\left( {1,2,3} \right),\left( {1,3,2} \right),\left( {2,1,3} \right),\left( {2,3,1} \right),\left( {3,1,2} \right),\left( {3,2,1} \right)} \right\}\)

d.

Let D represents the event that no one goes to station 2.

The possible outcomes for the event D is,

\(D = \left\{ {\left( {1,1,1} \right),\left( {1,1,3} \right),\left( {1,3,1} \right),\left( {1,3,3} \right),\left( {3,1,1} \right),\left( {3,1,3} \right),\left( {3,3,1} \right),\left( {3,3,3} \right)} \right\}\)