My Notes O Ask Your Teacher 2. -/6 points DevoreStat9 2.E.032. A stereo store is

Question

My Notes O Ask Your Teacher 2. -/6 points DevoreStat9 2.E.032. 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? (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

Explanation / Answer

5 type of receiver

4 type of CD player

3 type of speakars

4 type of turntable

(A) number of ways component of each type is selected = 5 * 4 * 3 * 4 = 240

(B) Here receiver and CD player is of sony so number of ways components to be selected = 3 *4 = 12

(C) Number of ways when Sony cannot be selected = 4 * 3 * 3 * 3 = 108

(D) At least one sony is to be selected = Total number of ways where each type is selected - Total number of ways when Sony is not to be selcted = 240 - 108 = 132

(E) Pr(At least one sony component) = 132/240 = 0.55

Number of ways exactly one component = Receiver is sony * No other sony components + CD palyer is sony * no other sony components + Turntable is sony * no other sony components = 3 * 3* 3 + 4 * 3 * 3 + 4 * 3 * 3 = 99

Pr(Exactly one sony comonent) = 99/240 = 0.4125

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