To determine the expected number of times each section of the spinner will be landed on, we can use the concept of probability.

Given:

• The spinner has 6 equal-size sections.
• The spinner is spun 30 times.

Since the spinner is fair, each section has an equal probability of being landed on. The probability of landing on any one section is:

$\frac{1}{6}$

For 30 spins, the expected number of times that any single section is landed on is calculated by multiplying the probability of landing on that section by the total number of spins:

$\text{Expected number of times} = \frac{1}{6} \times 30 = 5$

Answer:

The expected number of times that each section will be landed on is 5.

Would you like further details on this calculation or have any additional questions?

Here are five related questions to expand on this topic:

1. What would the expected number of times be if the spinner had 8 sections instead of 6?
2. How does the expected value change if the spinner is spun 100 times?
3. What is the probability of landing on each section in a single spin?
4. How would the variance in results change with more or fewer spins?
5. If each section had a different probability, how would we calculate the expected times for each section?

Tip: In probability problems, knowing the total number of outcomes and the probability of each outcome helps in calculating expected values efficiently.