Question
Days
Animals
Tigers Monkeys Total
Weekdays 34 25 59
Weekends 56 65 121
Total 90 90 180
Use the table to answer the following questions. Round your answers to the nearest percent.
Let event A be a person likes tigers, and event B be a person prefers weekdays.
First, find the probability of a person liking tigers, given that they prefer weekdays. P(A|B) is about
%.
Answers
GPT-4o mini
To find the probability \( P(A|B) \), which represents the probability of a person liking tigers given that they prefer weekdays, we can use the formula for conditional probability:
\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]
Where:
- \( P(A \cap B) \) is the probability of a person liking tigers and preferring weekdays.
- \( P(B) \) is the probability of a person preferring weekdays.
From the table, we know:
- The number of people who like tigers and prefer weekdays is 34 (the value in the "Tigers" row under "Weekdays").
- The total number of people who prefer weekdays is 59 (the total in the "Total" column under "Weekdays").
**Calculating \( P(A \cap B) \)**:
The probability of liking tigers and preferring weekdays is:
\[
P(A \cap B) = \frac{\text{Number of people who like tigers and prefer weekdays}}{\text{Total number of people}} = \frac{34}{180}
\]
**Calculating \( P(B) \)**:
The probability of preferring weekdays is:
\[
P(B) = \frac{\text{Total number of people who prefer weekdays}}{\text{Total number of people}} = \frac{59}{180}
\]
Now we can plug these values into the conditional probability formula:
\[
P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{34/180}{59/180} = \frac{34}{59}
\]
Now, we calculate \( \frac{34}{59} \):
\[
\frac{34}{59} \approx 0.5763
\]
To express this as a percentage, we multiply by 100:
\[
P(A|B) \approx 0.5763 \times 100 \approx 57.63\%
\]
Rounding to the nearest percent, we get:
\[
P(A|B) \approx 58\%
\]
Thus, the final answer is:
\[
P(A|B) \text{ is about } 58\%.
\]
\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]
Where:
- \( P(A \cap B) \) is the probability of a person liking tigers and preferring weekdays.
- \( P(B) \) is the probability of a person preferring weekdays.
From the table, we know:
- The number of people who like tigers and prefer weekdays is 34 (the value in the "Tigers" row under "Weekdays").
- The total number of people who prefer weekdays is 59 (the total in the "Total" column under "Weekdays").
**Calculating \( P(A \cap B) \)**:
The probability of liking tigers and preferring weekdays is:
\[
P(A \cap B) = \frac{\text{Number of people who like tigers and prefer weekdays}}{\text{Total number of people}} = \frac{34}{180}
\]
**Calculating \( P(B) \)**:
The probability of preferring weekdays is:
\[
P(B) = \frac{\text{Total number of people who prefer weekdays}}{\text{Total number of people}} = \frac{59}{180}
\]
Now we can plug these values into the conditional probability formula:
\[
P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{34/180}{59/180} = \frac{34}{59}
\]
Now, we calculate \( \frac{34}{59} \):
\[
\frac{34}{59} \approx 0.5763
\]
To express this as a percentage, we multiply by 100:
\[
P(A|B) \approx 0.5763 \times 100 \approx 57.63\%
\]
Rounding to the nearest percent, we get:
\[
P(A|B) \approx 58\%
\]
Thus, the final answer is:
\[
P(A|B) \text{ is about } 58\%.
\]