A study conducted at a certain college shows that 62% of the schools graduates find a job in their chosen field within a year after graduation. Find the probability that among 9 randomly selected graduates, all of them find a job in his or her chosen field within a year of graduating. Round your answer to four decimal places.

We are given that the probability \( p \) of a graduate finding a job in their chosen field within a year is 62%, or \( p = 0.62 \). We are tasked with finding the probability that all 9 randomly selected graduates find a job in their chosen field.

This is a binomial probability problem where we are interested in the probability that all 9 graduates are successful. Since each graduate's outcome is independent, the probability of all 9 being successful is simply the product of the individual probabilities.

The formula for the probability of all graduates being successful is:

\[
P(\text{all 9 are successful}) = p^9
\]

Substituting the value of \( p = 0.62 \):

\[
P(\text{all 9 are successful}) = (0.62)^9
\]

Let me calculate that.

\[
P(\text{all 9 are successful}) \approx 0.0077
\]

Thus, the probability that all 9 graduates find a job in their chosen field is approximately **0.0077**.

Would you like further clarification or details on the steps involved?

Here are five related questions:
1. What is the probability that none of the 9 graduates find a job in their chosen field?
2. How would the probability change if 7 out of 9 graduates found a job?
3. What is the probability that at least one graduate does not find a job in their chosen field?
4. How does the probability change if the success rate is increased to 75%?
5. Can you find the probability that exactly 5 out of 9 graduates find a job in their chosen field?

**Tip**: For large sample sizes, the binomial distribution can be approximated by a normal distribution for easier computation!

A study conducted at a certain college shows that 62% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 9 randomly selected graduates, all of them find a job in his or her chosen field within a year of graduating. Round your answer to four decimal places.

Discover how to calculate the probability that all 9 graduates find jobs in their chosen field using a 62% success rate. This problem explores binomial probability concepts and applies key formulas for real-world scenarios. Ideal for high school students in Grades 10-12.

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