Question
Leila has 10 hip hop, 5 r&b, 4 pop, and 3 alternative rock songs on a playlist. Leila puts the playlist on shuffle with song repeats allowed and records the genre of each song that comes on. The table below summarizes her findings.
Question 1
What is the theoretical probability of the playlist shuffling to a pop song?
Responses
A
2 over 11
B
1 fourth
C
5 over 22
D
22 fourths
Question 2
What is the experimental probability of the playlist shuffling to a pop song?
Responses
A
2 over 11
B
1 fifth
C
1 half
D
1 over 11
Question 1
What is the theoretical probability of the playlist shuffling to a pop song?
Responses
A
2 over 11
B
1 fourth
C
5 over 22
D
22 fourths
Question 2
What is the experimental probability of the playlist shuffling to a pop song?
Responses
A
2 over 11
B
1 fifth
C
1 half
D
1 over 11
Answers
GPT-4o mini
To solve the questions, we need to determine the theoretical and experimental probabilities of the playlist shuffling to a pop song.
### Question 1: Theoretical Probability
First, we find the total number of songs in Leila's playlist:
- Hip hop songs: 10
- R&B songs: 5
- Pop songs: 4
- Alternative rock songs: 3
Total number of songs = 10 + 5 + 4 + 3 = 22
Next, we find the probability of picking a pop song. The number of pop songs is 4.
The theoretical probability (P) of selecting a pop song is calculated as follows:
\[ P(\text{Pop}) = \frac{\text{Number of Pop Songs}}{\text{Total Number of Songs}} = \frac{4}{22} \]
This simplifies to:
\[ P(\text{Pop}) = \frac{2}{11} \]
The correct response for Question 1 is **A: 2 over 11**.
### Question 2: Experimental Probability
The experimental probability is determined by examining the outcomes from Leila's recorded findings after shuffling the playlist. However, since the results of the experiment are not provided in your question, we cannot compute the exact experimental probability without that data.
If you had a count of how many times a pop song played versus the total number of songs that played, you could compute it as:
\[ \text{Experimental Probability (P)} = \frac{\text{Number of times a Pop Song played}}{\text{Total Number of songs played}} \]
If you have that data or results, please provide it so I can help compute the experimental probability. Based on possible options, if there were no pop songs or it played rarely in the examples recorded, one of the answers could be correct.
If I had to choose without specific experimental results, I would suggest you conduct the experiment and tally how many times a pop song comes up in your observations.
### Question 1: Theoretical Probability
First, we find the total number of songs in Leila's playlist:
- Hip hop songs: 10
- R&B songs: 5
- Pop songs: 4
- Alternative rock songs: 3
Total number of songs = 10 + 5 + 4 + 3 = 22
Next, we find the probability of picking a pop song. The number of pop songs is 4.
The theoretical probability (P) of selecting a pop song is calculated as follows:
\[ P(\text{Pop}) = \frac{\text{Number of Pop Songs}}{\text{Total Number of Songs}} = \frac{4}{22} \]
This simplifies to:
\[ P(\text{Pop}) = \frac{2}{11} \]
The correct response for Question 1 is **A: 2 over 11**.
### Question 2: Experimental Probability
The experimental probability is determined by examining the outcomes from Leila's recorded findings after shuffling the playlist. However, since the results of the experiment are not provided in your question, we cannot compute the exact experimental probability without that data.
If you had a count of how many times a pop song played versus the total number of songs that played, you could compute it as:
\[ \text{Experimental Probability (P)} = \frac{\text{Number of times a Pop Song played}}{\text{Total Number of songs played}} \]
If you have that data or results, please provide it so I can help compute the experimental probability. Based on possible options, if there were no pop songs or it played rarely in the examples recorded, one of the answers could be correct.
If I had to choose without specific experimental results, I would suggest you conduct the experiment and tally how many times a pop song comes up in your observations.