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On his drive to work, John listens to one of 3 radio

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On his drive to work, John listens to one of 3 radio [#permalink] New post 05 Nov 2005, 23:40
On his drive to work, John listens to one of 3 radio stations A, B, or C. He turns to A first, If A is playing the song he likes he listens to it or changes to B, If he likes the song B is playing, he listens to it or changes to C, If he likes the song C is playing then he listens to it or he shuts the Radio off. For each station, the probability is 0.3 that at any given moment the station is playing a song that John likes. What is the probability that John will hear a song that he likes.
a) 0.027
b) 0.090
c) 0.417
d) 0.657
e) 0.90

Can somebody please explain this problem Thanks. I have my GMAT in a couple of days.
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 [#permalink] New post 05 Nov 2005, 23:50
I got D 0.657

3/10+(7/10*3/10)+(7/10*7/10*3/10) = 657/1000

you just need to add each positive case, whe the radio is playing his song.
1) Radio A
2) No RadioA*Radio B
3) No Radio A * No Radio B * Radio C
  [#permalink] 05 Nov 2005, 23:50
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On his drive to work, John listens to one of 3 radio

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