Problem Solving - 24

On his drive to work, Bob 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 Leo likes. On his drive to work, what is the probability that Bob will hear a song he likes?

A) 0.027
B) 0.090
C) 0.417
D) 0.657
E) 0.900

Answer: D

Probability Leo listens to A = (Probability that A is playing a song of Leo's choice ) = 0.3

Probability Leo listens to B = (Probability that A is not playing a song of Leo's choice ) * (Probability that B is playing a song of Leo's choice ) = (1-0.3) * 0.3 = 0.7*0.3

Probobility Leo listens to C = (Probability that A is not playing a song of Leo's choice ) * (Probability that B is not playing a song of Leo's choice ) * (Probability that C is playing a song of Leo's choice ) = 0.7 * 0.7 * 0.3

Total Probability = 0.3 + 0.7*0.3 + 0.7*0.7*0.3 = 0.657