Use the table to answer the question.

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.

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Answer 1

To find the percentage chance that a person who prefers cherries is from the North, we can use the formula for conditional probability.

First, we need to determine:

1. The total number of respondents who prefer cherries.
2. The number of respondents from the North who prefer cherries.

From the table:

• North prefers cherries: 120
• South prefers cherries: 25

Now, we can calculate the total number of respondents who prefer cherries:

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

Next, we determine the number of respondents from the North who prefer cherries, which is 120.

Now we can use the conditional probability formula:

\[ P(North | Cherries) = \frac{\text{Number of North cherries}}{\text{Total cherries}} = \frac{120}{145} \]

Now, let's calculate this fraction and convert it to a percentage:

\[ \frac{120}{145} \approx 0.8275862069 \]

Now, converting this to a percentage:

\[ 0.8275862069 \times 100 \approx 82.75862069 \]

Rounding this to the nearest tenth gives:

\[ \approx 82.8% \]

Thus, the percentage chance that a person who prefers cherries is from the North is 82.8%.