I would truly appreciate your help if you can go through the part (e) \"exactly

Question

I would truly appreciate your help if you can go through the part (e) "exactly one Sony component".

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? 192 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? 81 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 0.578 exactly one Sony component 0.333

Explanation / Answer

#E2

number of ways of selecting one component of every type
= 4 * 4 * 3 * 4 = 192 ways.

Number of ways in which we can get exactly one Sony component

= Onle receiver from sony + Only Compact disc player from Sony Brand + only Turntable from Sony brand

= 1 * 3 * 3 * 3 + 3 * 1 * 3 * 3 + 3 * 3 * 3 * 1 = 81.

probability of exactly one Sony component

= 81 / 192

= 27 / 64

= 0.422

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