Let's break this down to clarify the statements.

Spinner sections:

The spinner has six sections: 2, 2, 3, 4, 5, 6.

The probability of landing on odd-numbered sections:

• Odd-numbered sections: 3 and 5
• There are two odd-numbered sections out of six.

Therefore, the probability of landing on an odd-numbered section is:

$P(\text{odd}) = \frac{\text{Number of odd sections}}{\text{Total sections}} = \frac{2}{6} = \frac{1}{3} \approx 33.33\%$

The probability of landing on even-numbered sections:

• Even-numbered sections: 2, 2, 4, 6
• There are four even-numbered sections out of six.

Thus, the probability of landing on an even-numbered section is:

$P(\text{even}) = \frac{\text{Number of even sections}}{\text{Total sections}} = \frac{4}{6} = \frac{2}{3} \approx 66.67\%$

Let's review the statements:

1. The probability of landing on an odd-numbered section is 33.33%:

   • True. As calculated, this is correct.

2. The probability of landing on even-numbered sections is 66.67%:

   • True. As calculated, this is also correct.

3. It is less likely that the pointer will land on an odd-numbered section:

   • True. Since the probability of landing on an even-numbered section (66.67%) is higher than landing on an odd-numbered section (33.33%), this is correct.

4. It is impossible the pointer will land on 6:

   • False. One of the sections is numbered 6, so it is possible for the pointer to land on 6.

5. The spinner is fair:

   • False. A fair spinner would have an equal probability for each section. However, this spinner has two sections numbered 2, which makes it unfair as the chance of landing on 2 is higher than the chance of landing on other numbers.

Summary of true/false statements:

• The probability of landing on an odd-numbered section is 33.33%: True
• The probability of landing on even-numbered sections is 66.67%: True
• It is less likely that the pointer will land on an odd-numbered section: True
• It is impossible the pointer will land on 6: False
• The spinner is fair: False

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Would you like further explanation or examples on any of these points?

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Related questions:

1. What is the probability of landing on 2 or 4?
2. How would the spinner be modified to make it fair?
3. If the spinner had numbers 1 to 6, how would the probabilities change?
4. How does the total number of sections affect the probability calculations?
5. Can you calculate the expected number of times the pointer will land on an odd number if the spinner is spun 30 times?

Tip:

When evaluating the fairness of a spinner, ensure each section has an equal chance of being landed on. If any number appears more than once, the spinner is biased.