Giving a test to a group of students, the grades and gender are summarized below
\begin{tabular}{|r|r|r|r|r|}
\hline & A & B & C & Total \\
\hline Male & 18 & 14 & 5 & 37 \\
\hline Female & 9 & 13 & 12 & 34 \\
\hline Total & 27 & 27 & 17 & 71 \\
\hline
\end{tabular}

If one student is chosen at random,
Find the probability that the student got a 'B' GIVEN they are female.
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Step 1 ：Given a test to a group of students, the grades and gender are summarized in a table. If one student is chosen at random, we are asked to find the probability that the student got a 'B' given they are female.

Step 2 ：This question is asking for the conditional probability of a student getting a 'B' grade given that they are female. This can be calculated using the formula for conditional probability which is \(P(A|B) = \frac{P(A \cap B)}{P(B)}\). In this case, A is the event that the student got a 'B' and B is the event that the student is female.

Step 3 ：\(P(A \cap B)\) is the probability of both events A and B occurring which is the number of female students who got a 'B' divided by the total number of students. From the table, we know that the number of female students who got a 'B' is 13 and the total number of students is 71. So, \(P(A \cap B) = \frac{13}{71} = 0.183\).

Step 4 ：\(P(B)\) is the probability of event B occurring which is the total number of female students divided by the total number of students. From the table, we know that the total number of female students is 34 and the total number of students is 71. So, \(P(B) = \frac{34}{71} = 0.479\).

Step 5 ：Substitute \(P(A \cap B)\) and \(P(B)\) into the formula, we get \(P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.183}{0.479} = 0.382\).

Step 6 ：Final Answer: The probability that the student got a 'B' given they are female is \(\boxed{0.382}\).