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)?

a) 0.043
b) 0.053
c) 0.065
d) 0.074

Answer 1

The question seeks the probability of a randomly chosen farmer living in the Midwest and growing vegetables, represented by P(V ∩ M). Specific data from the two-way table is required to perform the calculation, which is missing, and thus the exact value cannot be given without this information.

Step-by-step explanation:

The student is asking about the probability of a randomly chosen farmer from the survey living in the Midwest and growing vegetables. This is known as finding the joint probability. However, specific data is missing from the two-way table mentioned in the question, which is crucial for calculating P(V ∩ M).

Without this data, we cannot provide the exact value of P(V ∩ M). To calculate P(V ∩ M), we would need to divide the number of farmers who live in the Midwest and grow vegetables by the total number of surveyed farmers.

Suppose the two-way table showed that there were 64 farmers in the Midwest who grow vegetables, then we would calculate P(V ∩ M) as 64 divided by 1,477, which would give us an approximate probability of 0.043, corresponding to option (a). However, this is purely hypothetical as the necessary data is not provided in the question.