N2015 P2 Q6

‘Droppers’ are small sweets that are made in a variety of colours. Droppers are sold in packets and the colours of the sweets in a packet are independent of each other. On average, \(25\%\) of Droppers are red.

1. A small packet of Droppers contains \(10\) sweets. Find the probability that there are at least \(4\) red sweets in a small packet.[2]

A large packet of Droppers contains \(100\) sweets.

2. Use a suitable approximation, which should be stated, to find the probability that a large packet contains at least \(30\) red sweets.[3]
3. Yip buys \(15\) large packets of Droppers. Find the probability that no more than \(3\) of these packets contain at least \(30\) red sweets.[2]