Question

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 %.

Answer 1

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

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

1. Find \( P(A \cap B) \): This is the probability of selecting a brown cat. From the table, there are 9 brown cats.

2. Find \( P(B) \): This is the probability of selecting a cat. The total number of cats is 38.

Now, substituting into the formula:

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

Calculating this gives:

\[ P(A|B) \approx 0.2368 \]

To express this as a percentage, multiply by 100:

\[ P(A|B) \approx 0.2368 \times 100 \approx 23.68% \]

Rounding to the nearest whole number:

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

So the final answer is:

\[ P(A|B) \text{ is } 24% . \]