According to a survey of 95,515 first-time freshmen enrolled at four-year colleges, 52,803 reported that they were enrolled at their first-choice college.
(a)
If a person who participated in this survey is selected at random, what is the probability that the selected person was enrolled at their first-choice college? (Round your answer to four decimal places.)
0.5529
 
Incorrect: Your answer is incorrect.
(b)
What is the probability that the selected person was not enrolled at their first-choice college? (Round your answer to four decimal places.)
0.4471
 
Incorrect: Your answer is incorrect.

Let's walk through this problem step by step to understand how to correctly calculate the probabilities.

### Part (a)
We are asked to find the probability that a randomly selected student was enrolled at their first-choice college.

The total number of students surveyed is:
\[
\text{Total number of students} = 95,515
\]

The number of students who reported that they were enrolled at their first-choice college is:
\[
\text{Number of students enrolled at their first-choice college} = 52,803
\]

The probability that a randomly selected student was enrolled at their first-choice college is calculated as the ratio of the number of students enrolled at their first-choice college to the total number of students:
\[
P(\text{enrolled at first-choice}) = \frac{52,803}{95,515}
\]

Let me calculate this for you.

\[
P(\text{enrolled at first-choice}) = \frac{52,803}{95,515} \approx 0.5528
\]

Thus, the correct probability rounded to four decimal places is:
\[
P(\text{enrolled at first-choice}) \approx 0.5528
\]

### Part (b)
Next, we are asked to find the probability that the selected person was **not** enrolled at their first-choice college.

The probability that a person was not enrolled at their first-choice college is simply:
\[
P(\text{not enrolled at first-choice}) = 1 - P(\text{enrolled at first-choice})
\]

Substituting the result from part (a):
\[
P(\text{not enrolled at first-choice}) = 1 - 0.5528 = 0.4472
\]

Thus, the correct probability rounded to four decimal places is:
\[
P(\text{not enrolled at first-choice}) \approx 0.4472
\]

### Summary:
- (a) The probability that the selected student was enrolled at their first-choice college is **0.5528**.
- (b) The probability that the selected student was not enrolled at their first-choice college is **0.4472**.

Would you like more details, or do you have any further questions on this?

### Related Questions:
1. How would the probabilities change if the total number of students were 100,000?
2. What is the complement rule, and how is it used to find the probability in part (b)?
3. If 60,000 students were enrolled at their first-choice college, what would the probability be?
4. How do you calculate probabilities when dealing with larger sample sizes?
5. What role does rounding play in probability calculations?

### Tip:
When solving probability problems, always make sure that the sum of complementary probabilities equals 1.

According to a survey of 95,515 first-time freshmen enrolled at four-year colleges, 52,803 reported that they were enrolled at their first-choice college.
(a) If a person who participated in this survey is selected at random, what is the probability that the selected person was enrolled at their first-choice college? (Round your answer to four decimal places.)
(b) What is the probability that the selected person was not enrolled at their first-choice college? (Round your answer to four decimal places.)

Calculate the probability that a randomly selected student was enrolled at their first-choice college based on a survey of 95,515 first-time freshmen. This problem explores probability concepts and the complementary rule. Suitable for Grades 9-12.

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