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# On his drive to work, Leo listens to one of three radio stat

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Intern
Joined: 18 Jul 2010
Posts: 40
On his drive to work, Leo listens to one of three radio stat  [#permalink]

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Updated on: 09 Jul 2013, 09:08
2
8
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:52) correct 26% (01:59) wrong based on 242 sessions

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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

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Originally posted by alexn49 on 11 Nov 2010, 08:00.
Last edited by Bunuel on 09 Jul 2013, 09:08, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
Posts: 56304

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11 Nov 2010, 08:04
5
1
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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Intern
Joined: 18 Jul 2010
Posts: 40

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11 Nov 2010, 08:06
Like the second option.
You are damn fast!
Thanks a lot!
Manager
Joined: 01 Nov 2010
Posts: 116
Location: Zürich, Switzerland

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11 Nov 2010, 13:07
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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20 Aug 2018, 11:48
1
alexn49 wrote:
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 probability that Leo will hear a song he likes on the way to work is the probability he will not turn off his radio. That is, either station A will be on for the entire trip, or station B or C will be on by the end of the trip.

The probability that station A will be on for the entire trip is 0.3.

Station B will be on by the end of the trip if station A did not play a song he likes AND station B did play a song he likes. The probability is 0.7 x 0.3 = 0.21.

Station C will be on by the end of the trip if station A did not play a song he likes AND station B did not play a song he likes AND station C did play a song he likes. The probability is 0.7 x 0.7 x 0.3 = 0.147.

Since these events are mutually exclusive, we add their probabilities, so the probability that a station will be on by the end of the trip is 0.3 + 0.21 + 0.147 = 0.657.

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Re: On his drive to work, Leo listens to one of three radio stat   [#permalink] 20 Aug 2018, 11:48
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