So I tried the book solution for it, but it didn\'t workout. Please solve correc

Question

So I tried the book solution for it, but it didn't workout. Please solve correctly!

6. 21 points I Previous Answers 92.E.032 My Notes Ask Your A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is ottered a choice of manufacturer for each component: Recelver: Kenwood, Onkyo, Ploneer, Sony, Sherwood Compact disc player: Onkyo, Pioneer, Sony, Technics Speakers: Poston, Infinity Turnlable: Onkyo, Sony, Teac, Technics A switchboard display in the store allows a customer to hook together any selection of components(consisting ot 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? X ways (h) In how many ways can components he selected if hoth the receiver and the compact disc player are to be Sony? 12 Xways (c) In hw ay ways can cumponerils be selected if one is lo be Sony? x ways (d) In how many ways can a selection be made if at least one Sony component is to be included? X ways (e) If someone flips switches on the selection in a completely random fashion, what is the probability that the systern selected contains at least one Sony comiponent? Exactly one Sony component? (Round your answer to three decimal places.) at least one Sony component exactly one Sony component 0412 Need Help?Read ItTalk to a Tutor

Explanation / Answer

a) Number of ways one can select each type of component = 5 * 4 * 2 * 4 = 160

b) Number of ways one can select component if both receiver and compact disc player is to be Sony = 1 * 1 * 2 * 4 = 8

c) Number of ways components can be slected if none is to be Sony = 4 * 3 * 2 * 3 = 72

d) Number of ways components can be slected if at least one Sony component is to be included = Number of ways one can select each type of component - Number of ways components can be slected if none is to be Sony

                                = 160 - 72

                                = 88

e) P(at least one Sony component) = 88/160 = 0.55

P(exactly one Sony component) = P(receiver component of Sony) + P(compact disc player of Sony) + P(turntablle of Sony)

                                     = (1 * 3 * 2 * 3)/160 + (4 * 1 * 2 * 3)/160 + (4 * 3 * 2 * 1)/160

                                     = 0.413

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