Probability Question...On his drive to work, Leo listen...?

Question

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 0.30 that any given moment the station is playing a song he likes. On his drive to work, what is the probability that Leo will hear a song he likes?

Answer 1

Take the probability of liking song A: .30
Add it to the probability of both listening to song B and then liking it: (1 - .30) (.30)
Add that to the probability of listening to song C and liking it:
(1 - (.30 + (1 - .30)(.30))) (.30)

Or, more simply,
The chance that Leo will like song A is 30%
Of the 70% of the time that he switches to station B, he will like the song 30% of the time. Thirty percent of 70% is 21%.
Of the 49% (100% - 30% - 21%) of the time Leo switches to station C, he will like the song 30% of the time. Thirty percent of 49% is 14.7%.
30% + 21% + 14.7 = 65.7% chance Leo will be boogie-ing to the tunes in his ride.

Answer 2

It's just like 3 tosses of a loaded die. The probabilities are independent of each other, so the prob. that he finds no station to his liking is 0.7^3. (He must go through all 3 stations to do this.) Thus the prob. that he finds what he wants is 1-0.7^3=0.657.

Answer 3

.3 + (1-.3)*.3 + (1-(1-.3)*.3)*.3