6) A study shows that 65% of the graduates from college find a job in the first month after graduation. Find the probability that among 4 randomly selected graduates, at least one finds a job in the first month after graduation.

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**Probability of Graduates Finding a Job in the First Month**

**Problem Statement:**
A study shows that 65% of the graduates from college find a job in the first month after graduation. Find the probability that among 4 randomly selected graduates, at least one finds a job in the first month after graduation.

**Solution Approach:**
To solve this problem, we will use the concept of complementary probability. The probability that at least one graduate finds a job can be calculated by first finding the probability that none of the selected graduates find a job, then subtracting this probability from 1.

1. **Probability of Not Finding a Job:**
   - Given that 65% of graduates find a job, the probability that a graduate does not find a job is \(1 - 0.65 = 0.35\).

2. **Probability of None of the 4 Graduates Finding a Job:**
   - Since the graduates are selected randomly and independently, the probability that all 4 graduates do not find a job is \(0.35^4\).

3. **Calculate \(0.35^4\):**
   - \(0.35^4 \approx 0.015\)

4. **Probability that At Least One Graduate Finds a Job:**
   - This is calculated as \(1 - \text{Probability that none find a job}\).
   - \(1 - 0.015 = 0.985\).

**Conclusion:**
Therefore, the probability that among 4 randomly selected graduates, at least one finds a job in the first month after graduation is approximately 0.985, or 98.5%.
Transcribed Image Text:**Probability of Graduates Finding a Job in the First Month** **Problem Statement:** A study shows that 65% of the graduates from college find a job in the first month after graduation. Find the probability that among 4 randomly selected graduates, at least one finds a job in the first month after graduation. **Solution Approach:** To solve this problem, we will use the concept of complementary probability. The probability that at least one graduate finds a job can be calculated by first finding the probability that none of the selected graduates find a job, then subtracting this probability from 1. 1. **Probability of Not Finding a Job:** - Given that 65% of graduates find a job, the probability that a graduate does not find a job is \(1 - 0.65 = 0.35\). 2. **Probability of None of the 4 Graduates Finding a Job:** - Since the graduates are selected randomly and independently, the probability that all 4 graduates do not find a job is \(0.35^4\). 3. **Calculate \(0.35^4\):** - \(0.35^4 \approx 0.015\) 4. **Probability that At Least One Graduate Finds a Job:** - This is calculated as \(1 - \text{Probability that none find a job}\). - \(1 - 0.015 = 0.985\). **Conclusion:** Therefore, the probability that among 4 randomly selected graduates, at least one finds a job in the first month after graduation is approximately 0.985, or 98.5%.
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