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A certain traditional Chinese medicine research institute has developed a traditional Chinese medicine for treating disease $A$. In order to understand its effect on disease $A$, a double-blind experiment needs to be conducted. Sixty volunteers with disease $A$ are randomly divided into two groups. Group A uses this traditional Chinese medicine normally, while group B uses a placebo instead of the medicine. After the entire treatment period, the number of recovered individuals in groups A and B are 20 and 5, respectively.
$(1)$ Based on the given data, complete the $2\times 2$ contingency table below and determine whether there is a $99.9\%$ certainty that the use of this traditional Chinese medicine is related to the recovery from disease $A$.

|         | Recovered | Not Recovered | Total |
|---------|-----------|---------------|-------|
| Group A | 20        |               | 30    |
| Group B | 5         |               | 30    |
| Total   |           |               |       |

$(2)$ If the frequency of recovery in group B without medication (using a placebo instead of the medicine) is considered as the self-healing probability of this disease, now randomly select 3 individuals from the population with disease $A$, let $X$ be the number of individuals who can self-heal. Find the distribution table and mathematical expectation of $X$.

Given table:

| $\alpha $ | 0.100 | 0.05  | 0.01  | 0.005 | 0.001 |
|-----------|-------|-------|-------|-------|-------|
| $x_{\alpha }$ | 2.706 | 3.841 | 6.635 | 7.879 | 10.828 |

Formula: ${\chi}^{2}=\frac{n(ad-bc)^{2}}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$.

Note: Double-blind experiment: refers to an experiment in which both the tester and the subjects do not know the group to which the subjects belong (experimental group or control group). The analyst usually does not know which group the data being analyzed belongs to when analyzing the data. The purpose is to eliminate subjective bias and intervention preferences that may occur in the minds of the experimenter and participants. Placebo: refers to a substance that has no therapeutic effect, similar in appearance to the actual medication in the form of tablets, pills, or injections.

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