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. 0.649
B. 0.370
C. 0.597
D. 0.620



Answer :

To determine the probability that a randomly selected cow from Farm B has feed that includes seaweed, we need to use the data provided in the table. Let's go through the steps:

1. Identify the Relevant Counts:
- The number of cows in Farm B that have seaweed in their feed is 74.
- The total number of cows in Farm B is 114.

2. Set Up the Probability Calculation:
- The probability of an event is given by the ratio of the favorable outcomes to the total number of possible outcomes. Here, the favorable outcomes are the cows with seaweed feed from Farm B, and the total outcomes are all cows from Farm B.

3. Calculate the Probability:
[tex]\[ P(\text{Seaweed} \mid \text{Farm B}) = \frac{\text{Number of cows with seaweed in Farm B}}{\text{Total number of cows in Farm B}} = \frac{74}{114} \][/tex]

4. Interpret the Result:
[tex]\[ P(\text{Seaweed} \mid \text{Farm B}) \approx 0.649 \][/tex]

So, the probability that a randomly selected cow from Farm B has feed that includes seaweed is approximately 0.649.

Thus, the correct answer is:
A. 0.649