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
Calculate the probability that a randomly picked sweet from the sample is green.
Total number of sweets in the sample = 10 + 8 + 7 + 5 = 30
Number of green sweets = 8
Probability of picking a green sweet = Number of green sweets / Total number of sweets = 8 / 30 = 4/15
If there are 600 sweets in total in the large bag, estimate how many are likely to be yellow, based on the sample results.
Total number of sweets in the large bag = 600
Number of yellow sweets in the sample = 7
Probability of picking a yellow sweet = Number of yellow sweets / Total number of sweets in sample = 7 / 30
Estimated number of yellow sweets in the bag = Probability of yellow sweet × Total sweets in the bag = (7 / 30) × 600 = 140
Explanation
The probability of an event is calculated as the ratio of the number of favourable outcomes to the total number of outcomes. For part (i), the favourable outcome is picking a green sweet, and the total outcomes are the total sweets in the sample. For part (ii), the textbook explains that the application of statistical probability in the real world is usually based on evidence collected from a sample. Therefore, the probability calculated from the sample is applied to the entire population to estimate the expected number of yellow sweets in the large bag.