Finding minimum n for P(X=0) threshold

Questions requiring the smallest n such that the probability of zero occurrences falls below a given threshold (e.g., P(X=0) < 0.05 or P(X=0) < 0.01).

4 questions · Standard +0.3

2.04d Normal approximation to binomial 5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!

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CAIE S2 2011 June Q4

7 marks Standard +0.3

4 On average, 1 in 2500 people have a particular gene.

Use a suitable approximation to find the probability that, in a random sample of 10000 people, more than 3 people have this gene.
The probability that, in a random sample of \(n\) people, none of them has the gene is less than 0.01 . Find the smallest possible value of \(n\).

CAIE S2 Specimen Q5

7 marks Standard +0.3

5 On average, 1 in 2500 adults has a certain medical condition.

Use a suitable approximation to find the probability that, in a random sample of 4000 people, more than 3 have this condition.
In a random sample of \(n\) people, where \(n\) is large, the probability that none has the condition is less than 0.05 . Find the smallest possible value of \(n\).

CAIE S2 2004 November Q5

7 marks Standard +0.3

5 Of people who wear contact lenses, 1 in 1500 on average have laser treatment for short sight.

Use a suitable approximation to find the probability that, of a random sample of 2700 contact lens wearers, more than 2 people have laser treatment.
In a random sample of \(n\) contact lens wearers the probability that no one has laser treatment is less than 0.01 . Find the least possible value of \(n\).

CAIE S2 2015 November Q5

7 marks Standard +0.3

5 On average, 1 in 2500 adults has a certain medical condition.

Use a suitable approximation to find the probability that, in a random sample of 4000 people, more than 3 have this condition.
In a random sample of \(n\) people, where \(n\) is large, the probability that none has the condition is less than 0.05 . Find the smallest possible value of \(n\).