Question
What are your odds of getting at least one job interview if you submit 1-10 applications?
A.
34.1%
B.
46.2%
C.
61.7%
solve it
A.
34.1%
B.
46.2%
C.
61.7%
solve it
Answers
GPT-4o mini
To solve the problem, we'll assume there is a certain probability (p) of getting a job interview for each application you submit. We'll then use the complement probability approach to determine the odds of getting at least one interview after submitting 1-10 applications.
Let's denote \( p \) as the probability of securing at least one interview from a single application. Thus, the probability of not getting an interview from one application is \( q = 1 - p \).
If you submit \( n \) applications, the probability of not getting an interview from any of them is \( q^n \). Hence, the probability of getting at least one interview after submitting \( n \) applications is:
\[
P(\text{at least one interview}) = 1 - q^n
\]
Assuming some realistic values for \( p \) (since it wasn't provided). Let's say \( p = 0.1 \) (or 10% chance of getting an interview), hence \( q = 0.9 \) (90% chance of not getting an interview).
Now, we can calculate the probability of getting at least one interview for \( n = 1 \) to \( n = 10 \) applications:
1. **For \( n = 1 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^1 = 1 - 0.9 = 0.1 \quad (10\%)
\]
2. **For \( n = 2 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^2 = 1 - 0.81 = 0.19 \quad (19\%)
\]
3. **For \( n = 3 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^3 = 1 - 0.729 = 0.271 \quad (27.1\%)
\]
4. **For \( n = 4 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^4 = 1 - 0.6561 = 0.3439 \quad (34.39\%)
\]
5. **For \( n = 5 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^5 = 1 - 0.59049 = 0.40951 \quad (40.95\%)
\]
6. **For \( n = 6 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^6 = 1 - 0.531441 = 0.468559 \quad (46.86\%)
\]
7. **For \( n = 7 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^7 = 1 - 0.4782969 = 0.5217031 \quad (52.17\%)
\]
8. **For \( n = 8 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^8 = 1 - 0.43046721 = 0.56953279 \quad (57.95\%)
\]
9. **For \( n = 9 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^9 = 1 - 0.387420489 = 0.612579511 \quad (61.26\%)
\]
10. **For \( n = 10 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^{10} = 1 - 0.3486784401 = 0.6513215599 \quad (65.13\%)
\]
From these calculations, the probabilities of getting at least one job interview for 1 to 10 applications do not directly match any of the options provided (A, B, C), but most closely aligns with C (61.7%) when \( n = 9 \).
If you want to pick the best answer based on this example, the closest correct response appears to be:
- **C. 61.7%** (for 9 applications).
If you are looking for different assumptions for the probability of getting an interview, let me know!
Let's denote \( p \) as the probability of securing at least one interview from a single application. Thus, the probability of not getting an interview from one application is \( q = 1 - p \).
If you submit \( n \) applications, the probability of not getting an interview from any of them is \( q^n \). Hence, the probability of getting at least one interview after submitting \( n \) applications is:
\[
P(\text{at least one interview}) = 1 - q^n
\]
Assuming some realistic values for \( p \) (since it wasn't provided). Let's say \( p = 0.1 \) (or 10% chance of getting an interview), hence \( q = 0.9 \) (90% chance of not getting an interview).
Now, we can calculate the probability of getting at least one interview for \( n = 1 \) to \( n = 10 \) applications:
1. **For \( n = 1 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^1 = 1 - 0.9 = 0.1 \quad (10\%)
\]
2. **For \( n = 2 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^2 = 1 - 0.81 = 0.19 \quad (19\%)
\]
3. **For \( n = 3 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^3 = 1 - 0.729 = 0.271 \quad (27.1\%)
\]
4. **For \( n = 4 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^4 = 1 - 0.6561 = 0.3439 \quad (34.39\%)
\]
5. **For \( n = 5 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^5 = 1 - 0.59049 = 0.40951 \quad (40.95\%)
\]
6. **For \( n = 6 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^6 = 1 - 0.531441 = 0.468559 \quad (46.86\%)
\]
7. **For \( n = 7 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^7 = 1 - 0.4782969 = 0.5217031 \quad (52.17\%)
\]
8. **For \( n = 8 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^8 = 1 - 0.43046721 = 0.56953279 \quad (57.95\%)
\]
9. **For \( n = 9 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^9 = 1 - 0.387420489 = 0.612579511 \quad (61.26\%)
\]
10. **For \( n = 10 \):**
\[
P(\text{at least one interview}) = 1 - (0.9)^{10} = 1 - 0.3486784401 = 0.6513215599 \quad (65.13\%)
\]
From these calculations, the probabilities of getting at least one job interview for 1 to 10 applications do not directly match any of the options provided (A, B, C), but most closely aligns with C (61.7%) when \( n = 9 \).
If you want to pick the best answer based on this example, the closest correct response appears to be:
- **C. 61.7%** (for 9 applications).
If you are looking for different assumptions for the probability of getting an interview, let me know!