Specimen Paper P2 Q7

‘Bings’ are sweets that are sold in packets of \(6\). Each packet is made up of randomly chosen coloured sweets. On average \(10\%\) of Bings are yellow.

1. Explain why a binomial distribution is appropriate for modelling the number of yellow sweets in a packet. Find the probability that a randomly chosen packet of Bings contains no more than one yellow sweet.[3]
2. Kev buys \(90\) randomly chosen packets of Bings. Find the probability that at least \(80\) of these packets contain no more than one yellow sweet.[2]

On average the proportion of Bings that are red is \(p\). It is known that the modal number of red sweets in a packet is \(2\).

3. Use this information to find exactly the range of values that \(p\) can take.[4]