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a song Leo likes

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by sanju09 » Fri Apr 10, 2009 4:31 am
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 to B. If B is playing a song he likes, he listens to it; if not, he turns 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 0.3 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. 0.3
B. 0.21
C. 0.147
D. 0.343
E. 0.657


OA E
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by dmateer25 » Fri Apr 10, 2009 5:56 am
Probability station A has a song he likes = .3

Probability station B has a song he likes = probability station A doesn't * probability that station B does = .7 * .3 = .21

Probability station C has a song he likes = probability station A doesn't * probability station B doesn't * probability station C does = .7 * .7 * .3 = .147

.3 + .21 + .147 = .657

E
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by GID09 » Fri Apr 10, 2009 6:40 am
probabilty that he gets to listen to a song of his liking = 1 - probabilty that he doesn't get to listen to a song of his liking

Given that probabilty that he doesn't get to listen to a song of his liking in ONE station is = 1- 0.3 = 0.7. In all 3 stations = 0.7*0.7*0.7 = 0.343

So, probabilty that he gets to listen to a song of his liking = 1-0.343 = 0.657

Hence E
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