2. Crispy-crisps produces packets of crisps. During a promotion, a prize is placed in \(25 \%\) of the packets. No more than 1 prize is placed in any packet. A box contains 6 packets of crisps.
- Write down a suitable distribution to model the number of prizes found in a box.
- Write down one assumption required for the model.
- Find the probability that in 2 randomly selected boxes, only 1 box contains exactly 1 prize.
- Find the probability that a randomly selected box contains at least 2 prizes.
Neha buys 80 boxes of crisps.
- Using a normal approximation, find the probability that no more than 30 of the boxes contain at least 2 prizes.