Question
GOC is planning to put on the musical West Side Story. There are 20 singers auditioning for the musical, including Alicia and Juan. The director is interested in choosing a lead singer and a backup singer. What is the probability that Alicia is selected lead singer and Juan is selected backup singer?
Question 1 options:
1.5%
0.3%
2.8%
0.5%
Question 1 options:
1.5%
0.3%
2.8%
0.5%
Answers
GPT-4o mini
To find the probability that Alicia is selected as the lead singer and Juan is selected as the backup singer, we can calculate the total number of possible outcomes and the favorable outcomes.
1. **Total number of singers:** 20
2. **Choosing a lead singer:** There are 20 choices for the lead singer.
3. **Choosing a backup singer:** Once the lead singer is chosen, there are 19 remaining choices for the backup singer.
So, the total number of ways to choose a lead singer and a backup singer is:
\[
\text{Total Outcomes} = 20 \times 19 = 380.
\]
Alicia being chosen as the lead singer is 1 favorable outcome (since there is only one Alicia), and Juan being chosen as the backup singer is another fixed outcome (since there is only one Juan).
Thus there is only **1 favorable outcome** for the specific event where Alicia is chosen as the lead singer and Juan is chosen as the backup singer.
Now the probability \(P\) that Alicia is selected as the lead singer and Juan is selected as the backup singer is given by:
\[
P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{380}.
\]
To express this as a percentage:
\[
P = \frac{1}{380} \approx 0.00263.
\]
Now converting to a percentage:
\[
P \approx 0.00263 \times 100 \approx 0.263\%.
\]
Now, rounding this to one decimal place, this value does not exactly match any provided options, but the closest could be interpreted as **0.3%**.
Therefore, based on the given options, the answer would be:
**0.3%**.
1. **Total number of singers:** 20
2. **Choosing a lead singer:** There are 20 choices for the lead singer.
3. **Choosing a backup singer:** Once the lead singer is chosen, there are 19 remaining choices for the backup singer.
So, the total number of ways to choose a lead singer and a backup singer is:
\[
\text{Total Outcomes} = 20 \times 19 = 380.
\]
Alicia being chosen as the lead singer is 1 favorable outcome (since there is only one Alicia), and Juan being chosen as the backup singer is another fixed outcome (since there is only one Juan).
Thus there is only **1 favorable outcome** for the specific event where Alicia is chosen as the lead singer and Juan is chosen as the backup singer.
Now the probability \(P\) that Alicia is selected as the lead singer and Juan is selected as the backup singer is given by:
\[
P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{380}.
\]
To express this as a percentage:
\[
P = \frac{1}{380} \approx 0.00263.
\]
Now converting to a percentage:
\[
P \approx 0.00263 \times 100 \approx 0.263\%.
\]
Now, rounding this to one decimal place, this value does not exactly match any provided options, but the closest could be interpreted as **0.3%**.
Therefore, based on the given options, the answer would be:
**0.3%**.