QUESTION 1
Easy
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:
10 red sweets | 8 green sweets | 7 yellow sweets | 5 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 result.
SOLUTION
1
Note down the given data
Total sweets in the sample \(= 30\)
| Colour | Number of Sweets |
|---|---|
| Red | 10 |
| Green | 8 |
| Yellow | 7 |
| Blue | 5 |
2
(i) Find the probability of a randomly picked sweet being green
Number of green sweets \(= 8\)
Total sweets in sample \(= 30\)
\(P(Green) = \frac{8}{30} = \frac{4}{15}\)
The probability of picking a green sweet is \(\frac{4}{15}\).
Total sweets in sample \(= 30\)
\(P(Green) = \frac{8}{30} = \frac{4}{15}\)
The probability of picking a green sweet is \(\frac{4}{15}\).
3
Estimate how many sweets are likely to be yellow
Yellow sweets in sample \(= 7\)
Total sweets in sample \(= 30\)
\(P(Yellow) = \frac{7}{30}\)
Applying this proportion to the whole bag of 600 sweets, we get
Estimated yellow sweets \(= \frac{7}{30} × 600 = 140\)
Approximately \(140\) sweets in the large bag are likely to be yellow.
Total sweets in sample \(= 30\)
\(P(Yellow) = \frac{7}{30}\)
Applying this proportion to the whole bag of 600 sweets, we get
Estimated yellow sweets \(= \frac{7}{30} × 600 = 140\)
Approximately \(140\) sweets in the large bag are likely to be yellow.
🏆
Final Answer :
P(Green) \(= \frac{4}{15}\)
Estimated yellow sweets \(= 140\).
Concept Note
A sample represents a smaller group from a larger population. If a sample is random and fair, we can use its proportion to estimate the values for the whole population.
In this question, \(\frac{7}{30}\) of the sample sweets were yellow, so we estimated the same fraction out of 600 sweets.