Question

if a farmer is chosen at random, what is the probability that the farmer planted corn or lettuce?
a. $\frac{3}{10}$
b. $\frac{7}{10}$
c. $\frac{1}{2}$
d. $\frac{1}{1}$

Explanation:

Step1: Calculate the number of farmers who planted corn or lettuce

Use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here, \(n(\text{Corn}) = 5 + 10=15\), \(n(\text{Lettuce})=10 + 10 = 20\), and \(n(\text{Corn}\cap\text{Lettuce}) = 10\). So \(n(\text{Corn}\cup\text{Lettuce})=15+20 - 10=25\).

Step2: Calculate the probability

The probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of farmers is \(50\). So \(P=\frac{25}{50}=\frac{1}{2}\).

Answer:

C. \(\frac{1}{2}\)