To solve the problem in the image, we need to determine the expected number of times the spinner will land on the sections labeled G, A, C, or F when the spinner is spun 15 times.

Step 1: Identify the sections.

From the image, the spinner is divided into 8 equal sections, each labeled as follows:

• A
• B
• C
• D
• E
• F
• G
• H

Step 2: Determine the probability of landing on G, A, C, or F.

The sections of interest are G, A, C, and F, so there are 4 favorable outcomes out of 8 possible sections.

$\text{Probability of landing on G, A, C, or F} = \frac{4}{8} = \frac{1}{2}$

Step 3: Calculate the expected number of times the spinner will land on G, A, C, or F after 15 spins.

Since the probability of landing on one of these sections in a single spin is $\frac{1}{2}$, and there are 15 spins in total, the expected number of times the spinner will land on one of these sections is:

$\text{Expected number of times} = \text{Probability} \times \text{Number of spins} = \frac{1}{2} \times 15 = 7.5$

So, you would expect the spinner to land on G, A, C, or F 7.5 times out of 15 spins.

Would you like any further details or have any other questions?

Related Questions:

1. How would the expected number change if there were only 6 sections?
2. What is the probability of landing on any specific section (e.g., B or D) in a single spin?
3. How would the outcome change if the spinner is spun 30 times instead of 15?
4. If only G and C were counted as favorable, what would be the expected number of times it lands on these in 20 spins?
5. How does changing the number of sections affect the probability distribution?

Tip:

Always ensure to calculate the probability first before multiplying it by the total number of trials to find the expected number of successful outcomes.