Question

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

38 people chose a cat
20 people chose a brown animal

Answer 1

To find the conditional probability \( P(A|B) \), where event A is selecting a brown animal and event B is selecting a cat, we need to know how many people selected both a brown animal and a cat.

However, with the data you provided, we have the following:
- Total number of people who chose a cat (event B): 38 people
- Total number of people who chose a brown animal (event A): 20 people

To compute the conditional probability \( P(A|B) \), we use the formula:

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

Where:
- \( P(A \cap B) \) is the number of people who chose a brown cat.
- \( P(B) \) is the total number of people who chose cats.

Without the exact number of people who chose a brown cat, we cannot calculate \( P(A|B) \) accurately.

Assuming that among those 20 people who chose brown animals, there is a known number \( x \) of them that also chose cats, we can express the conditional probability as:

\[
P(A|B) = \frac{x}{38}
\]

To fully calculate this probability, you'll need to provide the number of people who chose brown cats. If you have that information, please share so we can finalize the calculation!