Use the table to answer the question.

Cats Dogs TOTAL
Gray 12 2 14
Brown 9 11 20
Multicolor 17 21 38
TOTAL 38 34 72
Using the two-way frequency table about your local animal shelter, find the conditional probability P(A|B) where event A is a person selects a brown animal and event B is a person selects a cat. Round your answer to the nearest whole number.

(1 point)
P(A|B) is
%.

1 answer

To find the conditional probability \( P(A|B) \), where event \( A \) is selecting a brown animal and event \( B \) is selecting a cat, we use the formula:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Step 1: Identify \( P(A \cap B) \)

Here, \( P(A \cap B) \) represents the probability of selecting a brown cat. From the table:

  • Number of brown cats = 9

Step 2: Identify \( P(B) \)

\( P(B) \) represents the total probability of selecting a cat. From the table:

  • Total number of cats = 38

Step 3: Calculate \( P(A|B) \)

Now we calculate \( P(A|B) \):

\[ P(A|B) = \frac{\text{Number of brown cats}}{\text{Total number of cats}} = \frac{9}{38} \]

Step 4: Convert to percentage and round

To express this as a percentage:

\[ P(A|B) = \frac{9}{38} \times 100 \approx 23.68% \]

Rounding to the nearest whole number:

\[ P(A|B) \approx 24% \]

Thus, the final answer is:

\[ \boxed{24%} \]