A spinner has 4 equal sections: red, blue, green, and yellow. If we spin the spinner 28 times, what is the expected number of times the spinner will land on the colour blue?

To find the expected number of times the spinner will land on blue after 28 spins, we can use the concept of expected value in probability.

### Step-by-step process:

1. **Probability of landing on blue**:  
   Since the spinner has 4 equal sections (red, blue, green, and yellow), the probability of landing on blue in one spin is:

   \[
   P(\text{blue}) = \frac{1}{4}
   \]

2. **Expected value formula**:  
   The expected value \(E\) for a number of spins \(n\) is given by the formula:

   \[
   E = n \times P(\text{blue})
   \]

3. **Substitute values**:  
   Here, \(n = 28\) (number of spins) and \(P(\text{blue}) = \frac{1}{4}\):

   \[
   E = 28 \times \frac{1}{4} = 28 \div 4 = 7
   \]

### Conclusion:
The expected number of times the spinner will land on blue after 28 spins is **7 times**.

Would you like any more details, or do you have any questions?

Here are 5 related questions to further explore this concept:
1. What is the expected number of times the spinner will land on red in 40 spins?
2. What is the probability of the spinner landing on either red or blue in one spin?
3. If you spin the spinner 100 times, what is the probability of landing on blue at least 30 times?
4. How would the expected value change if there were 5 sections on the spinner instead of 4?
5. What is the variance in the number of times the spinner will land on blue after 28 spins?

**Tip**: Expected value gives the average outcome over many trials, but actual outcomes can vary due to randomness!

Discover how to calculate the expected number of times a spinner will land on blue after 28 spins. This problem covers probability concepts and expected value calculations, ideal for students in Grades 6-8. Learn with a clear, step-by-step solution.

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