
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The 19th Asian Games will open in Hangzhou on September 23, 2023. There are a total of 40 major events, 61 sub-events, and 482 minor events in this Asian Games. To investigate students' understanding of the Asian Games events, a university conducted a sampling survey. If the number of male and female students surveyed is both $10n$ ($n \in \mathbb{N}^*$), the following $2 \times 2$ contingency table was obtained, and after calculation, it was found that $K^{2} \approx 4.040$.

\[
\begin{array}{|c|c|c|c|}
\hline
& \text{Male} & \text{Female} & \text{Total} \\
\hline
\text{Understand} & 6n & \_\_\_\_ & \_\_\_\_ \\
\hline
\text{Do not understand} & \_\_\_\_ & 5n & \_\_\_\_ \\
\hline
\text{Total} & 10n & 10n & \_\_\_\_ \\
\hline
\end{array}
\]

$(1)$ Find the value of $n$ and determine with what confidence it can be said that the students' understanding of the Asian Games events is related to gender.

$(2)$ 
1. To understand the reasons why students do not understand the Asian Games events, a stratified sampling method was used to randomly select 9 students who do not understand the Asian Games events. From these 9 students, 3 students were selected for face-to-face communication. What is the probability of "at least one female student" being selected?
   
2. Considering frequencies as probabilities and using samples to estimate the population, 10 students were randomly selected from all students of the school. Let $X$ be the number of students who understand the Asian Games events among the 10 selected students. Find the expected value of the random variable $X$.

Given: 

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
P(K^{2} \geq k_{0}) & 0.10 & 0.05 & 0.025 & 0.010 & 0.001 \\
\hline
k_{0} & 2.706 & 3.841 & 5.024 & 6.635 & 10.828 \\
\hline
\end{array}
\]

Where ${K}^{2} = \frac{n{(ad-bc)}^{2}}{(a+b)(c+d)(a+c)(b+d)}$.

Present the answer in LaTex format: \boxed{Your answer}
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