A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. Class 9

A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. Class 9

Question 1.

A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. She counts the number of sweets of each colour: Class 9

10 red sweets 18 green sweets

7 yellow sweets 15 blue sweets

i. Calculate the probability that a randomly picked sweet from the sample is green.

ii. If there are 600 sweets in total in the large bag, estimate how many are likely to be yellow, based on the sample results.

Solution:

Total number of sweets = 30

Number of green sweets = 8

P(Green sweet) = $\frac{\text { Number of green sweets }}{\text { Total number of sweets }}$

$\begin{aligned} & =\frac{8}{30} \\ & =\frac{4}{15}\end{aligned}$

= 0.267

ii. Number of Yellow sweets in sample = 7

Total sweets in sample = 30

P(Yellow sweets) = $\frac{7}{30}$

∴ Estimated yellow sweets in 600 sweets

= $\frac{7}{30}$ × 600 = 140 30

∴ 140 sweets are likely to be yellow.