Giving a test to a group of students, the grades and gender are summarized below. Round your answers to 4 decimal places.

Grades and Gender
A	B	C	Total
Male	17	12	2	31
Female	10	18	16	44
Total	27	30	18	75

If one student is chosen at random, find the probability that the student got an 'B' GIVEN they are male:

To find the probability that a randomly selected student got a 'B' given that they are male, we use the concept of conditional probability. The formula for conditional probability is:

\[
P(B \mid \text{Male}) = \frac{P(B \text{ and Male})}{P(\text{Male})}
\]

### Step 1: Calculate \( P(B \text{ and Male}) \)
- The number of males who got a 'B' is 12.
- The total number of students is 75.

So, \( P(B \text{ and Male}) \) is the probability that a student is both male and got a 'B':

\[
P(B \text{ and Male}) = \frac{12}{75}
\]

### Step 2: Calculate \( P(\text{Male}) \)
- The total number of male students is 31.

So, \( P(\text{Male}) \) is:

\[
P(\text{Male}) = \frac{31}{75}
\]

### Step 3: Calculate the conditional probability
Now, substitute the values into the conditional probability formula:

\[
P(B \mid \text{Male}) = \frac{\frac{12}{75}}{\frac{31}{75}} = \frac{12}{31}
\]

### Final Answer
\[
P(B \mid \text{Male}) = \frac{12}{31} \approx 0.3871
\]

So, the probability that the student got a 'B' given they are male is approximately **0.3871**.

Would you like more details or have any other questions?

Here are some related questions you might find helpful:
1. What is the probability of selecting a female student?
2. What is the probability that a randomly selected student got an 'A'?
3. What is the probability that a randomly selected student is male given they got a 'C'?
4. What is the probability that a randomly selected student got an 'A' or is female?
5. What is the joint probability of selecting a male student who got an 'A'?

**Tip:** When dealing with probabilities, especially in conditional cases, clearly identifying the total relevant population (in this case, all males) is key to accurate calculations.

Calculate the probability that a randomly selected student got a 'B' given they are male. Understand the concept of conditional probability using a detailed step-by-step solution. Suitable for students in Grades 9-12.

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