Question

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
Compact disc player: Onkyo, Pioneer, Sony, Panasonic
Speakers: Boston, Infinity, Polk
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?
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 probability that the system selected contains at least
one Sony component? Exactly one Sony component?

Answer 1

Answer:

Given that:

A chain of stereo stores is offering a special price on a complete set of components (receiver , compact disk player , speakers).

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