Textbook Chapter 9 - View and print as needed
Calculator Resource: Desmos Scientific Calculator

A test was given 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 & 20 & 11 & 49 \\
\hline Female & 12 & 2 & 6 & 20 \\
\hline Total & 30 & 22 & 17 & 69 \\
\hline
\end{tabular}

If one student is chosen at random from those who took the test, find the probability that the student got a 'a 'B" GIVEN they are male. Write your answer as a reduced fraction.
\[
P(B \mid \text { male })=
\]
Question Help: $\square$ Video

Step 1 ：The problem is asking for the conditional probability of a student getting a 'B' grade given that the student is male. The formula for conditional probability is \(P(A|B) = \frac{P(A \cap B)}{P(B)}\). In this case, A is the event of getting a 'B' grade and B is the event of being male.

Step 2 ：\(P(A \cap B)\) is the probability of both events happening, which is the number of male students who got a 'B' grade divided by the total number of students. From the table, we can see that the number of male students who got a 'B' grade is 20.

Step 3 ：\(P(B)\) is the probability of being male, which is the number of male students divided by the total number of students. From the table, we can see that the total number of male students is 49.

Step 4 ：Substitute these values into the formula to find the answer: \(P(B|male) = \frac{20}{49}\)

Step 5 ：The probability of a student getting a 'B' grade given that the student is male is approximately 0.408. However, the question asks for the answer as a reduced fraction. We need to convert this decimal to a fraction.

Step 6 ：Final Answer: The probability that a student got a 'B' grade given they are male is \(\boxed{\frac{20}{49}}\).