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. 0.370
B. 0.620
C. 0.649
D. 0.597



Answer :

To find the probability that a randomly selected cow from Farm B has its feed include seaweed, we need to use the data specific to Farm B.

We start by identifying the relevant figures from the table for Farm B:
- Total number of cows at Farm B: 114
- Number of cows at Farm B with seaweed in their feed: 74

The formula for probability is given by:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \][/tex]

In this context:
- The "Number of favorable outcomes" is the number of cows that are fed with seaweed at Farm B, which is 74.
- The "Total number of possible outcomes" is the total number of cows at Farm B, which is 114.

Applying these numbers to the probability formula:
[tex]\[ \text{Probability} = \frac{74}{114} \][/tex]

When we calculate this fraction, we get:
[tex]\[ \frac{74}{114} \approx 0.649 \][/tex]

Hence, the probability that a randomly selected cow from farm B has its feed include seaweed is approximately 0.649.

Thus, the correct answer is:
C. 0.649