Question

Based on respondents' locations in the North or South of the state, the table shows survey results regarding their preferred fruit (grapes or cherries).
Cherries Grapes
North 120 125
South 25 75
Examine the data from a survey about the part of the state people are from and the fruit they prefer. If a person prefers cherries, what is the percentage chance that they are from the North? Round your answer to the nearest tenth.

Answer 1

To find the percentage chance that a person who prefers cherries is from the North, we first need to determine the total number of people who prefer cherries and how many of those are from the North.

From the table, we can see:
- Cherries preferred in the North: 120
- Cherries preferred in the South: 25

First, we calculate the total number of people who prefer cherries:

\[
\text{Total Cherries} = \text{Cherries North} + \text{Cherries South} = 120 + 25 = 145
\]

Next, we find the number of cherries preferers from the North:

- Cherries from the North: 120

Now, we can calculate the percentage of people who prefer cherries and are from the North:

\[
\text{Percentage from North} = \left( \frac{\text{Cherries from North}}{\text{Total Cherries}} \right) \times 100
\]

Substituting in the values:

\[
\text{Percentage from North} = \left( \frac{120}{145} \right) \times 100 \approx 82.7586
\]

Rounding to the nearest tenth:

\[
\text{Percentage from North} \approx 82.8\%
\]

Thus, if a person prefers cherries, there is approximately an **82.8%** chance that they are from the North.