Respuesta :
Question:
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, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Turn table: Onkyo, Sony, Teac, Technics
Answer:
The answers to the questions are;
(a) 144
(b) 12
(c) 54
(d) 90
(e) 0.625, 0.4375
Step-by-step explanation:
We apply the multiplication rule to solve questions (a) to (d) as follows
a. In how many ways can one component of each type beselected?
Receiver = 3 ways
Compact disc = 4 ways
Speaker = 3 ways and
Turn table = 4 ways
Therefore we have
One component of each can be selected in
3 × 4 × 3 × 4 = 144 ways
Answer = 144 ways
b. In how many ways can components be selected if both the receiver and the compact disc player are to be Sony?
If the receiver MUST be Sony then that is one way out of 4
Similarly too for the compact disc player.
Therefore we have the following ways
1×1×3×4 = 12
Answer = 12 ways
c. In how many ways can components be selected if none is to be Sony?
If NONE is to be Sony, we then have to exclude Sony in our calculations as follows
Receiver becomes 2 ways
Compact disc is then 3 ways
Speaker remains the same 3 because no Sony there and
Turn table becomes 3
Therefore we have
2×3×3×3 = 54
Answer = 54 ways
d. In how many ways can a selection be made if at least one Sony component is to be included?
Here, we use the logic that if at least one is to be Sony then
(The number of ways of selecting one component) - (The number of ways where none is Sony)
= 144 - 54 = 90
Answer = 90 ways
e. If someone flips switches on the selection in a completelyrandom fashion, what is the probability that thesystem selected contains at least one Sony component?
The probability is (Number of required outcomes) ÷ (Number of possible outcomes) = 90/144 = 0.625
Answer = 0.625
Exactly one Sony component?
Here again we have
If the receiver MUST be Sony then
1×3×3×3 = 27
If the compact disc MUST be Sony we have after removing Sony from receiver and turn table
2×1×3×3 = 18
Similarly, if the turn table MUST be Sony, then after removing Sony from the receiver and compact disc
2×3×3=18
Total number of ways = 63
Probability = 63/144 = 0.4375
