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radio station

by dreamv » Thu Feb 23, 2012 11:25 pm
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 paying 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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by kul512 » Fri Feb 24, 2012 2:01 am
Following is the probability-

(He listens songs on A) OR (He listens songs on B) OR (he listens songs on C).

We need to add the probability of all three cases-
1) Probability that he listens song on Channel A= 0.3

2) Probability that he listens song on Channel B=he doesn't listen song on channel AX listen song on channel B
=(1-0.3)X0.3=0.7X0.3=0.21

3) Probability that he listens song on channel C= He doesn't listen song on channel AX he doesn't listen song on channel B X Listen song on channel C
=(1-0.3)X(1-0.3)X0.3=0.49X0.3=0.147

SO total=
[spoiler]0.3+0.21+0.147=0.657

Choose (D)[/spoiler]
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by Brent@GMATPrepNow » Fri Feb 24, 2012 6:53 am
dreamv 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 to B. If B is playing a song he likes, he listens to it; if not, he turns to C. If C is paying 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
Here's another approach.

P(likes a song) = 1 - P(likes no song)

P(likes no song) = P(doesn't like song on channel A AND doesn't like song on channel B AND doesn't like song on channel C)
= P(doesn't like song on channel A) X P(doesn't like song on channel B) X P(doesn't like song on channel C)
= (0.7)(0.7)(0.7)

Aside we can approximate this by recognizing that (0.7)(0.7) is about 0.5
So, (0.7)(0.7)(0.7) ~ (0.5)(0.7) ~ 0.35

So, P(likes no song) = 0.35

This means that P(likes a song) = 1 - 0.35
= 0.65

The closest answer is D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by kul512 » Fri Feb 24, 2012 5:40 pm
Brent@GMATPrepNow wrote:
dreamv 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 to B. If B is playing a song he likes, he listens to it; if not, he turns to C. If C is paying 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
Here's another approach.

P(likes a song) = 1 - P(likes no song)

P(likes no song) = P(doesn't like song on channel A AND doesn't like song on channel B AND doesn't like song on channel C)
= P(doesn't like song on channel A) X P(doesn't like song on channel B) X P(doesn't like song on channel C)
= (0.7)(0.7)(0.7)

Aside we can approximate this by recognizing that (0.7)(0.7) is about 0.5
So, (0.7)(0.7)(0.7) ~ (0.5)(0.7) ~ 0.35

So, P(likes no song) = 0.35

This means that P(likes a song) = 1 - 0.35
= 0.65

The closest answer is D

Cheers,
Brent

Definitely this approach is better.
Sometimes there is very fine line between right and wrong: perspective.
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