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A medicine is known to be $75 \%$ effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is cured by this medicine?
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The correct answer is:
$\frac{1023}{1024}$
Probabilty of medicine to cure a patient $=\frac{75}{100}=\frac{3}{4}$ Probability of curing at least one patient
$=1-\left[1-\frac{3}{4}\right]^{5}=1-\left(\frac{1}{4}\right)^{5}=1-\frac{1}{1024}=\frac{1023}{1024}$
$=1-\left[1-\frac{3}{4}\right]^{5}=1-\left(\frac{1}{4}\right)^{5}=1-\frac{1}{1024}=\frac{1023}{1024}$
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