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?

Question

Mathematics

Bianca Pittman

1 May, 16:35

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?

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Answers (1)

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Gary Bird · Answer 1

The probability that Leo will hear a song he likes is 0.90

Step-by-step explanation:

The probability that Leo will hear a song he like is that either one of the radio station play the song he likes (either A or B or C)

Probability for each station = 0.30

Probability (A play song Leo likes) = 0.30

Probability (B play song Leo likes) = 0.30

Probability (C play song Leo likes) = 0.30

Probability (either A or B or C) = 0.30 + 0.30 + 0.30 = 0.90