Question 1

We will use the formula for probability to solve this problem.

Step 1 — Probability of green sweet

Let's find the total number of sweets in the sample. We have 30 sweets in total. There are 8 green sweets.

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

$= \frac{8}{30}$

$= \frac{4}{15}$

$\boxed{\frac{4}{15}}$

Step 2 — Estimated yellow sweets in the bag

First, let's find the probability of picking a yellow sweet from the sample. There are 7 yellow sweets in the sample. The total number of sweets in the sample is 30.

$P(\text{yellow sweet}) = \frac{\text{Number of yellow sweets}}{\text{Total number of sweets in sample}}$

$= \frac{7}{30}$

Now, we use this probability to estimate the number of yellow sweets in the large bag. The large bag has 600 sweets in total.

$\text{Estimated yellow sweets} = P(\text{yellow sweet}) \times \text{Total sweets in bag}$

$= \frac{7}{30} \times 600$

$= 7 \times \frac{600}{30}$

$= 7 \times 20$

$= 140$

$\boxed{140 \text{ yellow sweets}}$

Answer

(i) The probability that a randomly picked sweet from the sample is green is $\frac{4}{15}$. (ii) Approximately 140 sweets are likely to be yellow in the large bag.