On his drive to work, Leo listens to one of three radio stat : GMAT Problem Solving (PS)
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On his drive to work, Leo listens to one of three radio stat

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Joined: 18 Jul 2010
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On his drive to work, Leo listens to one of three radio stat [#permalink]

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11 Nov 2010, 07:00
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On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?

A. 0.027
B. 0.090
C. 0.417
D. 0.657
E. 0.900
[Reveal] Spoiler: OA

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Last edited by Bunuel on 09 Jul 2013, 08:08, edited 1 time in total.
Renamed the topic and edited the question.
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11 Nov 2010, 07:04
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On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
A. 0.027
B. 0.090
C. 0.417
D. 0.657
E. 0.900

The desired probability is the sum of the following events:

A is playing the song he likes - 0.3;
A is not, but B is - 0.7*0.3=0.21;
A is not, B is not, but C is - 0.7*0.7*0.3=0.147;
$$P=0.3+0.21+0.147=0.657$$.

Or: 1-the probability that neither of the stations is playing the song he likes: $$P=1-0.7*0.7*0.7=0.657$$.

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11 Nov 2010, 07:06
Like the second option.
You are damn fast!
Thanks a lot!
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11 Nov 2010, 12:07
On a station, the probability of getting song of choice is - 3/10.
The probability of not getting the song of choice on any station therefore is - 7/10.

So,
Probability of getting a song of choice on at least one of the stations

= 1-Probability of not getting a song of choice while trying all 3 stations.
= 1 - (7/10)*(7/10)*(7/10)
= 1- 343/1000
= 657/1000
=.657

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Re: On his drive to work, Leo listens to one of three radio stat [#permalink]

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05 Feb 2016, 10:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: On his drive to work, Leo listens to one of three radio stat   [#permalink] 05 Feb 2016, 10:06
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