2. + -6 points DevoreStat9 2E032. My Notes Ask Your Teacher A stereo store is of

Question

2. + -6 points DevoreStat9 2E032. My Notes Ask Your Teacher 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, 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? 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? Read" LTalk to aTutol

Explanation / Answer

a)
Total number of ways to select = 5C1 * 4C1 * 3C1* 4C1 = 240

Ans: 240 ways

b)
There is only one selection possible for receiver and compact disc player. other two components need to be selected

Required number of ways to select = 1 * 1 * 3C1 * 4C1 = 12

Ans: 12 ways

c)
If none needs to be of Sony, there are only 4 receivers, 3 compact disc players and 3 Turntable availabe

Required number of ways to select = 4C1 * 3C1 * 3C1 * 3C1 = 108

Ans: 108 ways

d)
There are total 240 ways to select the set of components, however 108 out of them does not have any sony components

Hence, required number of ways to select = 240 - 108 = 132

e)
P(at least one sony component) = 132/240 = 0.55
P(exactly one sony component) = (3*3*3 + 4*3*3 + 4*3*3)/240 = 0.4125

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