A stereo store is offering a special price on a complete set of components (rece

Question

A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component: Receiver: Kenwood, Onkyo, Sony, Sherwood Compact disc player: Onkyo, Pioneer, Sony, Technics Speakers: Boston, Infinity, Polk Turntable: Onkyo, Sony, Teac, Technics A switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules to answer the following questions: (a) In how many ways can one component of each type be selected? ways (b) In how many ways can components be selected if both the receiver and the compact disc player are to be Sony? ways (c) In how many ways can components be selected if none is to be Sony? ways (d) In how many ways can a selection be made if at least one Sony component is to be included? ways (e) If someone flips switches on the selection in a completely random fashion, what is the probability that the system selected contains at least one Sony component? Exactly one Sony component? (Round your answer to three decimal places.) at least one Sony component exactly one Sony component

Explanation / Answer

a)

number of ways=4 choice for receiver*4 choice for CD player*3 coice for speakers*for Turntable 4 choices

=4*4*3*4=192

b)

number of ways =1*1*3*4=12

c)

number of ways =3*3*3*3=81

d)

number of ways =192-81=111

e)

probability that the system selected contains at least one Sony component=111/192=0.578

P(Exactly one Sony component)=81/192=0.422

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