(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?
(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?
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 52SE: A car wash offers the following optional services to the basic wash: clear coat wax, triple foam...
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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, 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.
(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.)
I already have at least one Sony componet which is .635. I just need help with extactly one sony component. Thank you!
Transcribed Image Text: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, 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?
144
ways
(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?
54
ways
(d) In how many ways can a selection be made if at least one Sony component is to be included?
90
(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 .635
exactly one Sony component
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From Part (a), the number of ways of one component of each type to be selected is 144 ways.
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