Question 3

A test was given to a group of students. The grades and shirt colors are summarized below
Table: Frequencies by grades and shirt color
\begin{tabular}{|c|c|r|r|r|}
\hline Shirt Color & A & B & C & Total \\
\hline Blue Shirt & W & 8 & 2 & 19 \\
\hline Red Shirt & 10 & 15 & 6 & 31 \\
\hline Total & 19 & 23 & 8 & 50 \\
\hline
\end{tabular}

If one student is chosen at random from those who took the test, .
Find the probability that the student was Red Shirt GIVEN they got a ' $C$ '.

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Step 1 ：A test was given to a group of students. The grades and shirt colors are summarized in a table.

Step 2 ：We are asked to find the probability that a student was wearing a red shirt given that they got a 'C'.

Step 3 ：From the table, we can see that the number of students who got a 'C' and were wearing a red shirt is 6.

Step 4 ：The total number of students who got a 'C' is 8.

Step 5 ：We calculate the probability by dividing the number of students who got a 'C' and were wearing a red shirt by the total number of students who got a 'C'.

Step 6 ：The calculation is \( \frac{6}{8} = 0.75 \)

Step 7 ：So, the probability that a student was wearing a red shirt given that they got a 'C' is \(\boxed{0.75}\).