Question

1-87b. while waiting for a bus after school, renae programmed her mp3 player to randomly play two songs from her playlist, below. assume that the mp3 player will not play the same song twice.

playlist
a. i love my mama (country) by the strings of heaven
b. don’t call me mama (country) duet by sapphire and hank tumbleweed
c. carefree and blue (r & b) by sapphire and prism escape
d. go back to mama (rock) duet by bjorn free and sapphire
e. smashing lollipops (rock) by sapphire

in the previous problem, you found 10 different possible song combinations. are each of the combinations of two songs equally likely? why is that important?

choose the best answer.

it is not possible to tell if it is equally likely to hear each combination. i think we need to know how long each song is in order to figure this out.

yes. the combinations are equally likely because there are five songs. 100% can be divided into 5 equal parts, so there is equal likelihood of hearing all the combinations.

no. the combinations are not equally likely. renae is more likely to hear country songs in every combination.

yes. the combinations are all equally likely. this is important because i can use basic theoretical probability calculations to find the probability of listening to different song combinations on the mp3.

Explanation:

La selección aleatoria sin repetición (combinaciones) de 2 canciones de 5 da lugar a que cada combinación tenga la misma probabilidad, ya que el MP3 elige al azar sin preferencias. Esto es crucial para usar teoría de probabilidad básica (como conteo de casos) para calcular probabilidades de combinaciones. La primera opción está errada (la duración no afecta la selección aleatoria de combinaciones), la segunda justificación es errada (no se divide 100% en 5, sino en 10 combinaciones, pero la igualdad de probabilidad se debe a la selección aleatoria), la tercera es errada (no hay preferencia por género). La cuarta es correcta: las combinaciones son igualmente probables y esto permite usar cálculos de probabilidad teórica.

Answer:

Yes. The combinations are all equally likely. This is important because I can use basic theoretical probability calculations to find the probability of listening to different song combinations on the MP3.