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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
On his drive to work, Leo listens to one of three radio stations A, B
[#permalink]
18 Sep 2022, 21:59
18 Sep 2022, 21:59
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Question Stats:
75% (01:42) correct
25% (00:55) wrong based on 4 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
A. 0.027
B. 0.090
C. 0.417
D. 0.657
E. 0.900
Re: On his drive to work, Leo listens to one of three radio stations A, B
[#permalink]
21 Sep 2022, 03:50
21 Sep 2022, 03:50
1
Expert Reply
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: \(P=1-0.7*0.7*0.7=0.657\).
Answer: D.
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: \(P=1-0.7*0.7*0.7=0.657\).
Answer: D.
gmatclubot
Re: On his drive to work, Leo listens to one of three radio stations A, B [#permalink]
21 Sep 2022, 03:50
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