Question

answer must be three decimal places

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, Pioneer, Sony, Sherwoocd 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? 240ways (b) In how many ways can components be selected if both the receiver and the compact disc player are to be Sony? 12 ways (c) In how many ways can components be selected if none is to be Sony? 108ways (d) In how many ways can a selection be made if at least one Sony component is to be included? 132ways (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 0.55 exactly one Sony component 0.275X

Answer 1

Number of receiver = 5

Number of compact disc(CD) =4

Number of speakers = 3

Number of turanable = 4

a) Number of ways one component of each type be selected = 5*4*3*4 = 240

b) Number of ways can one component be selected if receiver and CD are to be sony = 1*1*3*4 = 12

c) number of ways can components be selected if none is to be sony = 4*3*3*3 = 108

d) Number of ways can a selection be made if at least one sony component is to be included = total - without sony component

= 240-108 =132

e) Probability that the system contains at least one sony component = 132/240 = 0.55

Number of ways to select exactly one sony component = only receiver is of sony + only CD is of sony + only turntable is of sony

= 1*3*3*3 + 4*1*3*3 + 4*3*3*1

= 99

Probability that the system contains exactly one sony component = 99/240 = 0.4125 = 0.413