A pharmacologist is testing a new drug and finds that it has a 70% chance of being effective on a single patient. If the drug is administered to four independent patients, what is the probability that the drug is effective on exactly two of them?

Sun, 03 May 2026 12:17:28 +0000

**A Pharmacologist’s Data: What’s the Chance a New Drug Works on Exactly Two Out of Four Patients?** When breakthrough treatments enter clinical trials, the numbers behind success can spark quiet curiosity. A pharmacologist recently reported a 70% effectiveness rate for a new drug tested on four independent patients. This figure alone raises compelling questions: What’s the likelihood the drug shows benefit in exactly two individuals? And why does this simple statistic matter to researchers, patients, and the broader healthcare landscape? This query isn’t just technical—it reflects a growing public and professional interest in meaningful treatment outcomes. As medical advancements accelerate, people are more aware of precision medicine and patient-specific responses. A drug with a 70% success rate invites deeper inquiry into probability, risk, and real-world application. For those navigating health decisions or researching innovations, understanding these probabilities supports informed expectations. ### The Math Behind the Probability