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25 June, 03:33

a disc jockey at a school dance had equal numbers of rock, country, and pop songs that she randomly selects from. she designs a simulation to estimate the probability that the next three songs she plays are all country songs. which simulation design could she use to estimate the probability?

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  1. 25 June, 05:48
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    The disc jockey can simply run a what is called a random experiment. In this experiment, she takes all the songs, and defines the probability of a particular song being played.

    Explanation:

    More specifically, in her random experiment, the DJ has a specific number of songs in total. Let's assume that she has 9 songs in total: 3 rock songs, 3 country songs, and 3 pop songs. We can assume this because the question says that she has an equal number of songs per genre.

    The probability of the first song being a country song is therefore 1/9, because the country song is 1 among 9 songs in total.

    The probability of the second song also being a country song is 1/8, because now, there are only 8 songs remaining,

    Finally, the probability of the third song also being a country song is 1/7, again, because now, there are only 7 songs remaining.

    Now, to find the probability of the first three songs all being country song, we multiply the above probabilities.

    1/9 * 1/8 * 1/7 = 1/504 or 0.19%.

    As we can see, the probability is extremely low.
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