2007 H2 Mathematics

Paper 2 Question 6

[This question has been adapted from the original for the new syllabus]

In a large population, $24 %$ have a particular gene $A,$ and $0.3 %$ have gene $B$

(a)

Find the probability that, in a random sample of $10$ people from the population, at most $4$ have gene $A .$

[2]

(b)

* $100$ samples of $10$ people are taken from the population. Find the probability that more than $90$ of these samples have at most $4$ having gene $A .$

[3]

(c)

* A random sample of $1000$ people is taken from the population. Find the probability that at least $2$ but fewer than $5$ have gene $B .$

[2]