Question

Crystal's favorite playlist has 80 rock songs, 40 jazz songs, 25 country songs, 30 hip hop songs, and 45 classical music songs. Which of thesestatements is true?

Answer 1

The true statement is

2. If Crystal plays songs at random, she should expect over half of them to be jazz or classical music songs.

Analysis of the statements

1. If Crystal plays songs at random, she should expect twice as many rock songs as hip hop songs.

There are 80 rock songs and 30 hip hop songs.

80 is not equal to 2 * 30, so this statement is false.

2. If Crystal plays songs at random, she should expect over half of them to be jazz or classical music songs.

Jazz songs + Classical music songs = 40 + 45 = 85.

This is more than half of the total songs (240), so this statement is true.

Therefore, the only true statement is:

• If Crystal plays songs at random, she should expect over half of them to be jazz or classical music songs.

Answer 2

This problem tests the knowledge of the probability of a random event occuring: of playing a type of song from a variety of different song types

Thus, we have to compute the probability that each type of song is played.

To do this, we need to obtain the total number songs, as follows:

80 + 40 + 25 + 30 + 45 = 220

Thus, the probabilities are now easily computed as follows:

P(rock) = 80/220

P(jazz) = 40/220

P(country) = 25/220

P(hip hop) = 30/220

P(classical) = 45/220

Now:

Option 1 (the first statement in the options) claims that : P(rock) = 2 * P(hip hop)

However, 2 * P(hip hop)