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!