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 conditional - probability formula

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

Step2: Identify values from the table

From the two - way table, the number of farmers who live in the Midwest ($n(M)$) is $365$ (the total in the "Midwest" column). The number of farmers who live in the Midwest and grow vegetables ($n(V\cap M)$) is $251$.

Step3: Calculate the conditional probability

$P(V|M)=\frac{n(V\cap M)}{n(M)}=\frac{251}{365}$

Answer:

$\frac{251}{365}$