2025 VJC P2 Q7

A shop sells apples in bags of \(12\). The average number of unripe apples in a bag is \(2.16\).

1. State two assumptions needed for the number of unripe apples in a bag to be well modelled by a binomial distribution.[2]

A bag of apples is sold at a reduced price if more than \(3\) apples are unripe.

2. Find the probability that a randomly selected bag of apples is sold at a reduced price.[2]
3. Twenty bags of apples are selected at random. Find the probability that fewer than \(4\) of these bags will be sold at a reduced price.[1]

The shop also sells oranges in bags of \(n\) oranges. On average, the proportion of oranges that is unripe is \(0.16\). It is known that the modal number of unripe oranges in a bag is \(2\). Find the set of possible values of \(n\).[2]