Problem Solving

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?


Please explain.....

I would solve this using complementary events i.e. P(station does not play songs that he likes), which is 0.7 for each of the stations.

P(A`) AND P(B`) AND P(C`) = 0.7 * 0.7 * 0.7 = 0.343

P(At least one station plays the song he likes) = 1 - 0.343 = 0.657

Is this correct?

yes it should be correct....
the other way would be...

1. station A 0.3
2. station B 0.7x0.3 = 0.21
3. station C 0.7x0.7x0.3 = 0.147

1+2+3 = .657


but i think 1-p is a better way