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Mariah has a spinner with 10 equal sections, each numbered from 1 to 10. She determines about how many times the spinner will land on a number greater than 7 in 250 spins. Her work is shown below:

[tex]\[
\begin{aligned}
P(\text{number greater than 7}) &= \frac{\text{Numbers greater than 7}}{\text{Total number of sections}} \cdot \text{Number of spins} \\
&= \frac{4}{10} \cdot 250 \\
&= 100
\end{aligned}
\][/tex]

What mistake did Mariah make, if any?

A. Mariah has the formula reversed; it should be the total number of sections over the numbers greater than 7.

B. Mariah should have used a 3 in the numerator because there are 3 numbers greater than 7.

C. Mariah should multiply by the number of sections in the spinner rather than the total number of spins.

D. Mariah calculated the prediction correctly and did not make any mistakes.

Sagot :

GinnyAnswer
Let's carefully analyze the problem step-by-step to identify if Mariah made a mistake and, if so, what that mistake is.

### Step 1: Identify the Numbers Greater Than 7
The spinner has the numbers 1 through 10. We need to figure out how many of these numbers are greater than 7. The numbers greater than 7 are:
- 8
- 9
- 10

Thus, there are 3 numbers greater than 7.

### Step 2: Calculate the Probability
Mariah needs to calculate the probability of the spinner landing on a number greater than 7. The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore,

[tex]\[ P(\text{number greater than 7}) = \frac{\text{Number of numbers greater than 7}}{\text{Total number of sections}} = \frac{3}{10} \][/tex]

### Step 3: Determine the Expected Number of Spins
Mariah wants to know how many times the spinner will land on a number greater than 7 out of 250 spins. The expected number of spins for a particular outcome is calculated using the formula:

[tex]\[ \text{Expected number of spins} = P(\text{number greater than 7}) \times \text{Total number of spins} \][/tex]

Substituting the numbers we have:

[tex]\[ \text{Expected number of spins} = \left(\frac{3}{10}\right) \times 250 = 0.3 \times 250 = 75 \][/tex]

### Analysis of Mariah's Work
Mariah's calculation is shown as:

[tex]\[ P(\text{number greater than 7}) = \frac{\text{Number of numbers greater than 7}}{\text{Total number of sections}} \times \text{Number of spins} = \frac{4}{10}(250) = 100 \][/tex]

### Step 4: Identify the Mistake
The correct number of numbers greater than 7 is 3, not 4. Mariah mistakenly used 4 as the numerator in her probability calculation. Therefore, her mistake is that she should have used 3 in the numerator because there are 3 numbers greater than 7: 8, 9, and 10.

### Conclusion
The correct options given the mistake analysis are:

- Mariah should have used a 3 in the numerator because there are 3 numbers greater than 7.

So, the correct identification of Mariah's mistake is:

Mariah should have used a 3 in the numerator because there are 3 numbers greater than 7.
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