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 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?
0.027
0.090
0.417
0.657
0.900
反向思考更为简单。一减去完全听不到他喜欢的歌,1减去0.7的三次方。画一个数轴图更为清楚
从第二种开始就要考虑前一种的情况了,不能想得太简单
0.3 + (0.7)(0.3) + (0.7)(0.7)(0.3)=0.657.
另一种:the opposite of the desired event is "leo doesn't hear a song he likes". that probability is (0.7)(0.7)(0.7) = 0.7^3, or 0.343.
therefore, the desired probability is 1 - 0.343, or 0.657.