Question 15

The probability a rock song will be played first is 3/10.

In a playlist where there are multiple genres of songs, the probability that a rock song plays first can be calculated by determining the ratio of rock songs to the total number of songs. Given the correct answer is 3/10, this indicates that there are 3 rock songs out of a total of 10 songs in the playlist.

A) 3/4

This option suggests that 75% of the songs in the playlist are rock songs, which would imply a much larger number of rock songs compared to total songs. This is incorrect as it does not match the calculated probability based on the provided context.

B) 1/3

A probability of 1/3 would indicate that there are roughly 3 rock songs for every 9 total songs. However, this does not align with the correct calculation of 3/10, making this option incorrect.

C) 1/4

This option implies that there is one rock song for every four total songs, which is not consistent with the given context. The correct proportion is represented by 3 out of 10, thus making this choice inaccurate.

D) 3/10

This option accurately reflects the probability that a rock song will be played first, as it indicates that there are 3 rock songs in a total of 10 songs in the playlist. This matches the calculated probability.

E) 5/16

This option suggests that 5 out of 16 songs are rock songs, which does not fit the context provided. The ratio does not reflect the actual number of rock songs in relation to the total, rendering this option incorrect.

Conclusion

The correct answer of 3/10 indicates that there are 3 rock songs among 10 total songs, making it the appropriate choice for determining the probability of a rock song being played first. All other options misrepresent the ratio of rock songs to total songs, thus failing to accurately reflect the situation presented in the question.