2. -6 points DevoreStat9 2.E.032 My Notes Ask Your Teache A stereo store is offe
ID: 3317785 • Letter: 2
Question
2. -6 points DevoreStat9 2.E.032 My Notes Ask Your Teache 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, Sony, Sherwood Compact disc player: Onkyo, Pioneer, Sony, Technics Speakers: Boston, Infinity Turntable: Onkyo, Sony, Teac, Technics A switchbord 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 Need Help?Explanation / Answer
a) Total number of ways in which components could be selected here is computed as:
= Total number of receivers * Total number fo disk players * Total number of speakers * Total number of turntables
= 3*4*2*4
= 96
Therefore 96 ways are there in total here.
b) The number of ways in which components could be selected here such that both receiver and disc player are to be Sony is computed here as:
= Number of Speakers possible * Number of Turntables
= 2*4
= 8
Therefore 8 ways are there in total here.
c) None is to be sony, then the total number of possibilities here would be computed as:
= 2*3*2*3
= 36
Therefore 36 ways are there in total here.
d) At least one sony component must be included
= Total number of possibilities - Total number of possibilities without sony
= 96 - 36
= 60
Therefore 60 ways are there in total here.
e) Probability that the system contains at least one sony components here is computed as:
= Number of ways to select such that there is at least one sony component / Total number of selections possible
= 60 / 96
= 0.625
Therefore 0.625 is the required probability.
e) Exactly one sony component, number of ways here are computed as:
Therefore total number of ways here = 18 +12 + 12 = 42
Therefore the required probability here is computed as:
= 42 / 96
= 0.4375
Therefore 0.4375 is the required probability here.
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