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

[BTGmoderatorLU]

Source: GMAT Prep

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 OA is D.

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Hi All,

We're told that 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. We're asked for the probability that Leo will hear a song he likes. While this question is a bit wordy, it's based on standard Probability rules.

With Probability questions, there are two outcomes that you can calculate: what you WANT to happen and what you DON'T want to happen. Since the sum of those two fractions is always 1, sometimes the easiest way to calculate what you WANT to happen is to calculate what you DON'T want and then subtract that fraction from 1.

This question asks for the probability that Leo will hear a song that he likes among 3 options. Instead of calculating all of the different ways for that to occur, we'll calculate the probability that he does NOT hear a song that he likes on any of the stations...

Probability of hearing a song that he likes = .3
Probability of NOT hearing a song that he likes = 1 - .3 = .7

Probability of NOT hearing a song that he likes on ALL 3 stations = (.7)(.7)(.7) = (.7)(.49) = .343

Thus, the probability that he will hear a song that he likes is 1 - .343 = .657

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Jeff@TargetTestPrep]

Source: GMAT Prep

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.

Answer: D