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.

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.

GPT-4o mini · Answer

To find the percentage chance that a person who prefers cherries is from the North, we first need to calculate the total number of respondents who prefer cherries and those who prefer cherries from the North.

From the data provided:

Cherries from the North: 120
Cherries from the South: 25

Total respondents who prefer cherries: \[ 120 + 25 = 145 \]

Number of respondents who prefer cherries from the North: \[ 120 \]

Now, we can calculate the probability that a person who prefers cherries is from the North using the formula: \[ P(North | Cherries) = \frac{\text{Number of North respondents who prefer cherries}}{\text{Total number of respondents who prefer cherries}} \]

Substituting the values into the formula, we get: \[ P(North | Cherries) = \frac{120}{145} \]

Next, we calculate this value: \[ P(North | Cherries) \approx 0.8275862069 \]

To express this as a percentage, we multiply by 100: \[ P(North | Cherries) \times 100 \approx 82.75862069 \]

Rounding to the nearest tenth, the percentage chance that a person who prefers cherries is from the North is approximately: \[ \boxed{82.8} \]