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Question
Assume that a drug causes a serious side effect at a rate of three patients per one hundred. What is the probability that atleast one person will have side effects in a random sample of ten patients taking the drug?
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Solution
Here n = 10
p = `3/10`, q = `1 - "p" = 1 - 3/100`
q = `97/100`
The binomial distribution is P(X = x) = ncxpxqn-x
= `10"c"_x (3/100)^x (97/100)^(10 - x)`
Probability that atleast one person will have side effect
= P(X ≥ 1)
= `1 - "P"("X" < 1)`
= `1 - "P"("X" = 0)`
= `1 - [10"c"_0 (3/100)^0 (97/100)^(10 - 0)]`
= `1 - [(1)(1)(97/10)^10]`
= `1 - (0.97)^10`
= `1 - 0.4656`
= 0.5344
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