Question

an animal researcher randomly selected 98 dogs and cats and recorded if they napped between 2:00 p.m. and 2:30 p.m. the two - way table displays the data.
suppose an animal is randomly selected. let event c = cat and let event n = nap. what is the value of p(c|n)?

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(C|N)=\frac{P(C\cap N)}{P(N)}\). In the context of a two - way table, \(P(C\cap N)\) is the number of cats that nap divided by the total number of animals, and \(P(N)\) is the number of animals that nap divided by the total number of animals. So, \(P(C|N)=\frac{\text{Number of cats that nap}}{\text{Number of animals that nap}}\).

Step2: Identify the values from the table

From the table, the number of cats that nap (\(C\cap N\)) is \(23\), and the number of animals that nap (\(N\)) is \(38\).

Answer:

\(\frac{23}{38}\)