A medicine is known to be 75\% effective. If the medicine is given to 5 patients, what is the probability that at least one patient is cured? - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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A medicine is known to be 75% effective. If the medicine is given to 5 patients, what is the probability that at least one patient is cured?

Solution & Step-by-step Explanation

Success probability p = 75% = 3/4 .Failure probability q = 1 - p = 1/4 .Number of trials n = 5 .We need to find P (at least one cured) = 1 - P (none cured) . P (none cured) = P (X = 0) = (0 5) p^{0} q^{5} . P (X = 0) = 1 \cdot 1 \cdot (\frac{1}{4})^{5} = \frac{1}{1024} P (at least one) = 1 - \frac{1}{1024} = \frac{1023}{1024}

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A medicine is known to be 75% effective. If the medicine is given to 5 patients, what is the probability that at least one patient is cured?

1/1024

243/1024

1023/1024

781/1024

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