First, we need to determine the number of history students from each state. We will use the numbers directly from the table provided.
Here are the counts of history students by state:
- Texas: 30
- New York: 17
- Washington: 20
- Florida: 32
- Utah: 33
Next, we sum these values to find the total number of history students:
[tex]\[
30 + 17 + 20 + 32 + 33 = 132
\][/tex]
So, there are a total of 132 history students.
We specifically want the probability that the history student selected at random is from Washington. We already know there are 20 history students from Washington.
To find the conditional probability, we divide the number of history students from Washington by the total number of history students:
[tex]\[
\text{Probability} = \frac{\text{Number of history students from Washington}}{\text{Total number of history students}} = \frac{20}{132}
\][/tex]
To simplify the fraction:
[tex]\[
\frac{20}{132} = \frac{10}{66} = \frac{5}{33} \approx 0.1515
\][/tex]
Thus, the probability that the selected student is from Washington, given that the student studies history, is approximately:
[tex]\[
0.15151515151515152
\][/tex]
In conclusion, the probability that the student is from Washington, given that they study history, is approximately 0.1515 or [tex]\(\frac{5}{33}\)[/tex].
