A university is researching the impact of including seaweed in cattle feed. They assign feed with and without seaweed 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. 0.849
C. 0.370
D. 0.597



Answer :

To determine the probability that a randomly selected cow from Farm B has feed that includes seaweed, we need to look at the relevant data for only Farm B.

The table provides the following information for Farm B:
- Number of cows with seaweed in their feed: 74
- Total number of cows at Farm B: 114

The probability that a randomly selected cow from Farm B has feed that includes seaweed is calculated by dividing the number of cows with seaweed by the total number of cows at Farm B.

[tex]\[ \text{Probability} = \frac{\text{Number of cows with seaweed}}{\text{Total number of cows at Farm B}} = \frac{74}{114} \][/tex]

Performing this division gives us:
[tex]\[ \frac{74}{114} \approx 0.649 \][/tex]

Hence, the probability that a randomly selected cow from Farm B has feed that includes seaweed is approximately [tex]\(0.649\)[/tex].

Comparing this result to the given choices:
A. 0.620
B. 0.849
C. 0.370
D. 0.597

The closest match to our calculated probability is not exactly listed in the options. However, our calculated probability [tex]\(0.649\)[/tex] would correspond closely to [tex]\(0.64\)[/tex] if rounding considerations were taken into account, but we must select the best approximation from the provided choices, concluding there might be a typo or similar oversight in the provided choices or problem setup.

Given the available choices and accurate calculation, the correct probability value from our calculation doesn't align perfectly with the listed options.
Thus, based on the most accurate calculations, there might be a consideration outside the standard rounding approaches for this specific question set.