Problem 3: An electronics store is offering a special price on a complete set of

Question

Problem 3: An electronics store is offering a special price on a complete set of components (receiver, compact disc player, speakers). A purchaser is offered a choice of manufacturer for each component Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood Compact disc player: Onkyo, Pioneer, Sony Speakers: Boston, Infinity, Polk A switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the fundamental theorem of counting. (a) In how many ways can a set of components be selected? (b) In how many ways can a set of components be selected if receiver and player are to be Sony? (c) If a customer selects a complete set of components randomly, what is the probability that the selected set consists of a Sony receiver and a Sony player? (keep at least 4 decimal places) (d) If a customer selects a complete set of components randomly, what is the probability that the selected set consists of at least one Sony component? (keep at least 4 decimal places)

Explanation / Answer

a) number of ways =N(4 choice for Receiver)*N(3 chice for CD player)*N(3 choice for speakers)

=4*3*3=36

b)

as receiver and player are fixed therefore we can choose only speakers for which number of choices =3

c)

probability=3/36=0.0833

d)

P(at least one Sony component)=1-P(no Sony component)=1-(3*2*3)/36=1-0.5 =0.5

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