Question 5 A chain of stereo stores is offering a special price on a complete se

Question

Question 5 A chain of stereo stores is offering a special price on a complete set of components (receiver, com- pact disc player, speakers). A purchaser is offered a choice of manufacturer for each component: Receiver: Kenwood, Onkyo, Pioneer, Sony, Yamaha Onkyo, Pioneer, Sony, Panasonic Boston. Infinity, Polk Compact disc player: Speakers: A switchboard display in the store allows a cus- tomer to hook together any selection of compo- nents (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? b. In how many ways can components be selected if both the receiver and the compact disc player are to be Sony? c. In how many ways can components be selected if none is to be Sony? d. In how many ways can a selection be made if at least one Sony component is to be included? e. If someone flips switches on the selection in a completely random fashion, what is the proba- bility that the system selected contains at least one Sony component? Exactly one Sony com- ponent?

Explanation / Answer

a) Number of ways to select each component = 5 * 4 * 3 = 60

b) Number of ways to select components if both receiver and CD player is to be sony = 1 * 1 * 3 = 3

c) Number of ways to select components if none of the component is of Sony = 4 * 3 * 3 = 36

d) Number of ways to select components if atleast one of the component is of Sony = Number of ways to select each component - Number of ways to select components if none of the component is of Sony

                                                        = 60 - 36

                                                        = 24

e) P(at least one component is of Sony) = 24 / 60 = 0.4

P(exactly one component is of Sony) = P(only receiver is of Sony) + P(only CD player is of Sony)

                                                           = 3*3/60 + 4*3/60

                                                           = 0.35

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