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.

(1 point)

Answer 1

To find the percentage chance that a person who prefers cherries is from the North, we can use the following formula:

\[ P(North | Cherries) = \frac{P(North \cap Cherries)}{P(Cherries)} \]

First, we need to determine the total number of people who prefer cherries and those who are from the North who prefer cherries.

From the table:

• Number of people from the North who prefer cherries = 120
• Number of people from the South who prefer cherries = 25

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

\[ P(Cherries) = \text{(North Cherries)} + \text{(South Cherries)} = 120 + 25 = 145 \]

Now we can calculate \(P(North | Cherries)\):

\[ P(North | Cherries) = \frac{120}{145} \]

Next, we calculate the probability:

\[ P(North | Cherries) \approx 0.8276 \]

To convert this into a percentage,

\[ 0.8276 \times 100 \approx 82.76 \]

Rounding to the nearest tenth gives us:

\[ 82.8% \]

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