In: Statistics and Probability
A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, cassette deck). A purchaser is offered a choice of manufacturer for each component:
Receiver: | Kenwood, Onkyo, Sony, Sherwood |
Compact disc player: | Onkyo, Pioneer, Sony, Technics |
Speakers: | Boston |
Cassette deck: | 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?
(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?
What is the probability that the system contains exactly one Sony
component?