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Let's break down the problem using the data from the table.

The table shows grades (A, B, C) distributed between male and female students, and there are 54 students in total.

|       | A  | B  | C  | Total |
|-------|----|----|----|-------|
| Male  | 16 | 15 | 10 | 41    |
| Female|  6 |  5 |  2 | 13    |
| Total | 22 | 20 | 12 | 54    |

Now, let's solve the given questions:

### 1. Find the probability that the student got a B:
The total number of students who received a B is 20. The total number of students is 54. So, the probability is:

\[
P(B) = \frac{20}{54} = \frac{10}{27}
\]

### 2. Find the probability that the student was male **AND** got a C:
The number of male students who got a C is 10, and the total number of students is 54. Thus, the probability is:

\[
P(\text{Male AND C}) = \frac{10}{54} = \frac{5}{27}
\]

### 3. Find the probability that the student was female **OR** got a B:
For this, we use the formula for the union of two events:

\[
P(\text{Female OR B}) = P(\text{Female}) + P(B) - P(\text{Female AND B})
\]

- \( P(\text{Female}) = \frac{13}{54} \)
- \( P(B) = \frac{20}{54} \)
- \( P(\text{Female AND B}) = \frac{5}{54} \) (since 5 females got a B)

Thus,

\[
P(\text{Female OR B}) = \frac{13}{54} + \frac{20}{54} - \frac{5}{54} = \frac{28}{54} = \frac{14}{27}
\]

### 4. Find the probability that the student got a 'B' **GIVEN** they are male:
This is a conditional probability:

\[
P(B | \text{Male}) = \frac{P(\text{Male AND B})}{P(\text{Male})}
\]

- \( P(\text{Male AND B}) = \frac{15}{54} \)
- \( P(\text{Male}) = \frac{41}{54} \)

So,

\[
P(B | \text{Male}) = \frac{15}{41}
\]

---

Would you like any more details or clarifications on the solution?

Here are 5 additional related questions to deepen your understanding:
1. What is the probability that the student is female **AND** got an A?
2. What is the probability that a randomly chosen student is male **OR** got a C?
3. Find the probability that the student is **not** female, given they received a C.
4. If two students are chosen at random, what is the probability that both are males?
5. What is the probability that the student got an A **GIVEN** they are female?

**Tip:** When solving probability problems, make sure to identify whether you're dealing with independent events, conditional probabilities, or a combination of multiple conditions (like "AND" and "OR").

Given a test to a group of students, the grades and gender are summarized below. If one student is chosen at random, find the following probabilities:
1. The probability that the student got a B.
2. The probability that the student was male AND got a C.
3. The probability that the student was female OR got a B.
4. The probability that the student got a B GIVEN they are male.

Learn how to calculate probabilities based on a table of student grades and gender. This problem covers key concepts such as basic probability, conditional probability, and the union and intersection of events. Detailed solutions include finding the probability of a student getting a B, being male and getting a C, being female or getting a B, and the conditional probability of getting a B given the student is male.

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