SolarEdge Computing, a renowned Silicon Valley startup, is making waves with its innovative data encryption algorithms and unyielding commitment to security. Their prominence is largely due to the unique encryption keys they use, each batch containing $5000$ units, procured from a trusted local supplier in Palo Alto. The deal between SolarEdge and their supplier demands that no more than $3$ percent of the encryption keys in any batch be flawed, underscoring SolarEdge's strict security standards.

When a new batch of encryption keys arrives, SolarEdge's meticulous validation procedure kicks off. The first phase involves randomly selecting a sample of $50$ keys for initial analysis. If this test uncovers no flawed keys, the batch is immediately accepted, ensuring a smooth operational flow. If $5$ or more flawed keys are detected in this sample, the batch is outright rejected to uphold SolarEdge's high$-$security benchmarks. In cases where $1$ to $4$ flawed keys are discovered, a secondary test is undertaken with an additional $50$ keys. For the batch to clear this second round, it must contain no more than $2$ flawed keys. Surpassing this limit results in the batch's disapproval.

Given these strict security and quality protocols, what is the probability that SolarEdge will approve a batch of encryption keys, ensuring adherence to the stringent criteria set in their contract with the supplier?