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.