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, Onkyo, Sony, Sherwood
Compact disc player:	Onkyo, Pioneer, Sony, Technics
Speakers:	Boston, Infinity
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.

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?

Show all steps.

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Thanks

Answer 1

1)total number to select 1 of each type =N(select 1 from 4 Receiver )*N(select 1 from 4 Compact disc player )*N(select 1 from 2 speakers )*N(select 1 from 4 Cassette Deck )

=4*4*2*4=128

number of ways none of Sony =N(3 choice for Receiver except Sony)*N(3 choice for Compact disc player except Sony)*N(2 choice for speakers except Sony)*N(3 choice for Cassette Deck except Sony)*

=3*3*2*3=54

therefore number of system with at least one Sony component =128-54 =74

P( system selected contains at least one Sony component ) =74/128 =0.5781

2)

P(exact 1 of Sony)=P(only receiver)+P(only CD player)+P(only speakers)+P(only cassette deck)
=(1*3*2*3+3*1*2*3+3*3*0*3+3*3*2*1)/128=54/128 =0.4219