In a chicken farm, eggs are packed into boxes of $12$. In the transportation of the eggs from the fa

Question

In a chicken farm, eggs are packed into boxes of $12$. In the transportation of the eggs from the farm to a supermarket, it is found that on average, $k$ eggs out of $10$ eggs are broken on arrival at the supermarket. A box of eggs is randomly chosen for inspection. Find, in terms of $k$,

the expected number of eggs that are broken in the box,[1]
the probability that the ${{8}^{\mathrm{th}}}$ egg inspected is the ${{2}^{\mathrm{nd}}}$ egg that is broken.[2]

It is given that $k=0.8$.

Find the probability that there are not more than $2$ broken eggs in the box.[2]
If $n$ boxes are randomly selected for inspection, find the least value of $n$ such that the probability that at most $3$ boxes will have at least $3$ broken eggs is less than $0.9$.[3]

Accepted Answer

(i) $\dfrac{6k}{5}$; (ii) $\dfrac{7k^{2}}{100}\left(1-\dfrac{k}{10}\right)^{6}$; (iii) $0.935$; (iv) $n = 28$

2020 TJC P2 Q5

2020 TJC P2 Q5

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