N2026 P2 Q9

Tringos are sweets that are made in four different colours: red, yellow, purple and green. They are sold in packets containing \(12\) randomly chosen sweets.

1. A student wishes to estimate the proportion of Tringos that are green. She checks the contents of \(100\) randomly chosen packets of Tringos and finds the information summarised in the table.

   number of green sweets in a packet	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\) or more
   frequency	\(15\)	\(32\)	\(27\)	\(18\)	\(6\)	\(2\)	\(0\)

   Use the information in the table to estimate the probability that a randomly chosen Tringo is green.[2]

The probability that a randomly chosen Tringo is red is \(0.3\).

2. Find the probability that a packet of \(12\) Tringos contains fewer than \(5\) red sweets.[1]
3. Find the probability that at least \(4\) out of \(7\) randomly chosen packets of Tringos contain fewer than \(5\) red sweets.[2]

Tringos are delivered to shops in cartons containing \(72\) randomly chosen packets of \(12\) sweets.

4. Find the probability that there are more than \(250\) red sweets in a randomly chosen carton of Tringos.[2]

The probability that a randomly chosen Tringo is yellow is \(p\).

5. Given that the probability that a randomly chosen packet of \(12\) Tringos contains either \(2\) or \(3\) yellow sweets is \(0.206\), find the two possible values of \(p\). Give your values correct to 3 decimal places.[3]