A Los Angeles-area radio station plays songs from a specific, fixed set of artists. The station has no DJ; instead, a computer randomly selects which songs to play. The songs themselves are picked randomly, and the same song may be played many times in a row. In the set of songs, 55% are sung by a female singer, 35% are sung by a male singer, and 10% are instrumental with no vocals. What is the probability that a song with a female singer, a song with a male singer, and an instrumental song will be played in that order?

Question

Mathematics

Howard Schroeder

1 August, 11:03

A Los Angeles-area radio station plays songs from a specific, fixed set of artists. The station has no DJ; instead, a computer randomly selects which songs to play. The songs themselves are picked randomly, and the same song may be played many times in a row. In the set of songs, 55% are sung by a female singer, 35% are sung by a male singer, and 10% are instrumental with no vocals. What is the probability that a song with a female singer, a song with a male singer, and an instrumental song will be played in that order?

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Camila Massey · Answer 1

The events are * independent * (they can even be repeated any times). This means multiplication of individual probabilities:

P =.55*.35*.10 = 0.01925

You can't take any other order. That's all.