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

Answer: The answer is d.

Step-by-step explanation: Ok, so, we know that we have 3 radio stations, each one has a 30% chance of broadcasting a song that leo likes.

Lets see the cases:

Station A has a probability of 0.30 to broadcast a song, but let's suppose that it doesn't, then we go to station B, who has te same probability, 0.30, but for this to happen, we first must have the 0.70 prob of A to broadcasting another song, so here we have a probability of (0.30) * (0.70).

Now with a similar way of thinking, if Station B also fails, we will have a probability of 0.70*0.70*0.30 for Station C succes.

Also, there is the case were station A broadcast the nice song, which we already know that is with probability of 30%.

So, the total probability will be the sum of the 3 cases: 0.30 + 0.30*0.70 + 0.30*0.70*0.70 = 0.657.