A committee of 2 people is to be selected from 4 executives

A committee of 2 people is to be selected from 4 executives, Alam, Bartolini, Bartolini, Chinn , and Dickson. Write Write out the sample space S, choosing an S with equally likely outcomes, if possible. Then give the value of n(S) and tell whether the outcomes in S are equally likely. Finally, write the indicated events below in set notation.

a.

ChinnChinn

is on the committee.

b.

AlamAlam

and

ChinnChinn

are not both on the committee.

c. Both

AlamAlam

and

BartoliniBartolini

are on the committee.

What is the sample space? Use the first initial of each executive to write the events? The value of n(S) is? Are the outcomes equally likely? Write the event

ChinnChinn

is on the committee.

Solution

Sample space is given by S = {Alam, Bartolini, Chinn, Dickson} .

When two executives are choosen from the above set then equally likely outcomes are given by :

{Alam, Bartolini}, {Chinn, Dickson}, {Alam,Chinn}, {Alam,Dickson}, {Bartolini,Dickson} and {Bartolini, Chinn}.

Chinn is on the committee : {Chinn, Dickson}, {Alam,Chinn},{Bartolini, Chinn}.

Alam and Chinn are not both on the committee : {Bartolini,Dickson}

Both

Alam and Bartolini are on the committee : {Chinn, Dickson}