A university is researching the impact of including seaweed in cattle feed. They assign feed with and without seaweed to be fed to cows at two different dairy farms. The two-way table shows randomly collected data on 200 dairy cows from the two farms about whether or not their feed includes seaweed.

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & With Seaweed & Without Seaweed & Total \\
\hline
Farm A & 50 & 36 & 86 \\
\hline
Farm B & 74 & 40 & 114 \\
\hline
Total & 124 & 76 & 200 \\
\hline
\end{tabular}

Based on the data in the table, if a cow is randomly selected from farm B, what is the probability that its feed includes seaweed?

A. 0.620
B. 0.370
C. [tex]$0.597$[/tex]
D. 0.649



Answer :

To determine the probability that a randomly selected cow from Farm B has feed that includes seaweed, follow these steps:

1. Identify the total number of cows in Farm B:
From the table, we see that Farm B has a total of 114 cows.

2. Identify the number of cows in Farm B that are fed with seaweed:
The table shows that Farm B has 74 cows that are given feed with seaweed.

3. Calculate the probability:
The probability is found by dividing the number of cows with seaweed by the total number of cows in Farm B:
[tex]\[ \text{Probability} = \frac{\text{Number of cows with seaweed in Farm B}}{\text{Total number of cows in Farm B}} = \frac{74}{114} \][/tex]

4. Simplify the fraction or convert to a decimal:
Performing the division gives:
[tex]\[ \frac{74}{114} \approx 0.649 \][/tex]

Therefore, the probability that a randomly selected cow from Farm B has feed that includes seaweed is closest to option D. [tex]\(0.649\)[/tex].

Answer: D. [tex]\(0.649\)[/tex]