Conditional Binomial Probability Scenario

00:00 5 marks

A pharmaceutical company is testing a new drug. In a clinical trial of 10 patients, the probability that a patient shows improvement is 0.3, independent of other patients. Given that at least 2 patients show improvement, calculate the probability that exactly 3 patients improve. Provide your answer in exact form and as a decimal rounded to three decimal places.

Hint Hint

Hint

Use the conditional probability formula along with the binomial probability function.

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Answer Answer

Complete Answer

\(\frac{\binom{10}{3}(0.3)^3(0.7)^7}{1-(0.7)^{10}-10\cdot0.3\cdot(0.7)^9}\) \(\approx 0.314\)

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