On average $8$% of cherries sold in supermarkets are rotten. A customer randomly selected $26$ c

Question

On average $8$% of cherries sold in supermarkets are rotten. A customer randomly selected $26$ cherries from a large number of cherries. State, in context, two assumptions for the number of rotten cherries in the sample to be well-modelled by a binomial distribution.[2] Find the most likely number of rotten cherries that the customer could have picked.[2] Another customer randomly selected $n$ cherries such that the probability of having at most one rotten cherry is less than $0.1$. Express this information as an inequality in $n$, and hence find the smallest possible integer value of $n$.[3] The cherries are packed in boxes, each containing $60$ cherries. Find the probability that a randomly chosen box contains at most one rotten cherry.[3]

Accepted Answer

(i) Independent outcomes and constant probability 0.08. (ii) 2 rotten cherries. (iii) $0.92^n+n(0.08)(0.92)^{n-1}<0.1$; least integer $n=48$. (iv) $0.0418$.

2015 CJC P2 Q6

2015 CJC P2 Q6

Solution:

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