Question

a researcher randomly surveyed 1,477 farmers to determine the geographical region in which they farm and the types of crops that grow there. the two - way table displays the data.

suppose a farmer from this survey is chosen at random. let m = farmer lives in the midwest and v = farmer grows vegetables. what is the value of p(v|m)?

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(V|M)=\frac{P(V\cap M)}{P(M)}\). In terms of counts from the two - way table, \(P(V|M)=\frac{\text{Number of farmers who grow vegetables and live in the Midwest}}{\text{Number of farmers who live in the Midwest}}\).

Step2: Identify the relevant values from the table

From the table, the number of farmers who grow vegetables and live in the Midwest (\(V\cap M\)) is \(251\), and the number of farmers who live in the Midwest (\(M\)) is \(365\).

Answer:

\(\frac{251}{365}\approx0.6877\)