A healthcare organisation is sharing medical research data with a research partner while ensuring privacy protection using a privacy$-$preserving technique called $"$k$-$anonymity." The dataset contains information about patients' medical conditions and their ages. The organisation wants to disclose aggregate statistics about patient ages while protecting individual privacy.

The organisation chooses to achieve $3-$anonymity, meaning that there are at least three patients with the same age and medical condition for any combination of age and medical condition. The dataset contains the following information:

$$ Patient A: Age $45,$ Medical Condition X

$$ Patient B: Age $30,$ Medical Condition Y

$$ Patient C: Age $45,$ Medical Condition Z

$$ Patient D: Age $35,$ Medical Condition X

$$ Patient E: Age $50,$ Medical Condition Y

$$ Patient F: Age $45,$ Medical Condition X

$$ Patient G: Age $30,$ Medical Condition Z

$$ Patient H: Age $30,$ Medical Condition X

a$)$ Calculate the transformed dataset that satisfies the $3-$anonymity requirement. $[3]$

b$)$ Explain how the transformed dataset ensures privacy protection for individual patients. $[1]$