You have a spinner with four even-sized sections. The sections are labeled 1, 2, 3, 4. You spin the spinner twice. What is the probability of landing on 4 at least once?
 
Hint: a tree diagram may help with this.
 
Provide your answer as a decimal rounded to the nearest hundredth.

To find the probability of landing on 4 at least once when spinning the spinner twice, we can use complementary probability. Instead of calculating the probability of landing on 4 at least once directly, we'll first calculate the probability of not landing on 4 in both spins, and then subtract that from 1.

### Step-by-Step Solution:

1. **Probability of not landing on 4 in one spin:**
   - There are 4 sections labeled 1, 2, 3, and 4.
   - The probability of not landing on 4 in one spin is the probability of landing on 1, 2, or 3.
   \[
   P(\text{not 4}) = \frac{3}{4}
   \]

2. **Probability of not landing on 4 in both spins:**
   - Since the spins are independent, the probability of not landing on 4 in both spins is:
   \[
   P(\text{not 4, not 4}) = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16}
   \]

3. **Probability of landing on 4 at least once:**
   - This is the complement of the event "not landing on 4 in both spins."
   \[
   P(\text{at least one 4}) = 1 - P(\text{not 4, not 4}) = 1 - \frac{9}{16} = \frac{7}{16}
   \]

4. **Decimal form:**
   - Convert \(\frac{7}{16}\) to a decimal.
   \[
   \frac{7}{16} = 0.4375
   \]
   Rounding 0.4375 to the nearest hundredth gives 0.44.

### Final Answer:

The probability of landing on 4 at least once is:

\[
0.44
\]

Would you like more details on any of the steps, or do you have further questions? Here are some related questions you might find useful:

1. What is the probability of landing on 4 exactly once?
2. What is the probability of landing on the same number twice?
3. How does the probability change if the spinner has unequal sections?
4. What is the probability of landing on numbers 1 and 4 in any order?
5. If you spin three times, what is the probability of landing on 4 at least once?

**Tip:** Using complementary probability (finding the probability of the opposite event and subtracting from 1) can simplify calculations, especially when dealing with "at least one" type of questions.

You have a spinner with four even-sized sections. The sections are labeled 1, 2, 3, 4. You spin the spinner twice. What is the probability of landing on 4 at least once?

Calculate the probability of landing on 4 at least once when spinning a spinner with four sections labeled 1, 2, 3, and 4, twice. This problem uses complementary probability and independent events concepts, making it suitable for Grades 6-8 students. The final answer is rounded to 0.44.

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