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To solve the problem:

You are asked to estimate how many pieces of vanilla cake are likely to be taken in the next 30 samples based on past data. Here's how to approach this:

### Given dataTo solve the problem:

You are asked to estimate how many pieces of vanilla cake are likely to be taken in the next 30 samples based on past data. Here's how to approach this:

### Given 
- 4 pieces of vanilla cake have been taken.
- 6 pieces of coconut cake have been taken.

This means the total number of pieces already taken is \( 4 + 6 = 10 \).

The probability that a passerby takes a vanilla cake is:

\[
P(\text{vanilla}) = \frac{4}{10} = 0.4
\]

Now, we are asked how many pieces of vanilla cake we should expect from the next 30 samples. The expected number of vanilla pieces is the product of the total number of samples (30) and the probability of selecting a vanilla piece:

\[
\text{Expected vanilla pieces} = 30 \times 0.4 = 12
\]

Thus, you can expect 12 pieces of vanilla cake out of the next 30 samples.

Would you like further details or explanations on any part of this? Here are some additional questions for you:

1. How do probabilities affect sampling predictions in larger datasets?
2. What if more flavors were introduced, how would that change the calculation?
3. How would the result change if more coconut cake had been taken?
4. Can this method be applied to non-cake-related probability scenarios?
5. What is the significance of using past data to predict future outcomes?

**Tip:** Always ensure that the total probability sums to 1 when dealing with proportions or percentages.

Passersby have taken 4 pieces of vanilla cake and 6 pieces of coconut cake from a sample tray. Based on past data, of the next 30 samples taken, how many should you expect to be pieces of vanilla cake?

Learn how to calculate the expected number of vanilla cake pieces in a sample, based on probability and past data. Understand the concept of expected value with an example involving a sample tray of vanilla and coconut cake pieces. Suitable for students in Grades 5-7.

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