To find the probability that a randomly chosen student got a 'C' given that they are female, we are looking for a conditional probability.

The formula for conditional probability is:

$P(C \mid F) = \frac{P(C \cap F)}{P(F)}$

Where:

• $P(C \mid F)$ is the probability of getting a 'C' given the student is female.
• $P(C \cap F)$ is the probability of both being female and getting a 'C'.
• $P(F)$ is the probability of being female.

Step 1: Find $P(C \cap F)$

From the table, the number of females who got a 'C' is 4. Since the total number of students is 56, the probability of a female student getting a 'C' is:

$P(C \cap F) = \frac{4}{56}$

Step 2: Find $P(F)$

The total number of females is 31, so the probability of being female is:

$P(F) = \frac{31}{56}$

Step 3: Calculate the Conditional Probability

Now, using the conditional probability formula:

$P(C \mid F) = \frac{\frac{4}{56}}{\frac{31}{56}} = \frac{4}{31}$

So, the probability that the student got a 'C' given they are female is:

$P(C \mid F) = \frac{4}{31}$

Would you like further details on this calculation or any additional clarification?

Here are 5 related questions for you to explore further:

1. What is the probability that a student chosen at random is male?
2. What is the probability that a student got an 'A' given they are female?
3. What is the probability that a student chosen at random got a 'B'?
4. What is the probability that a student got an 'A' given they are male?
5. What is the probability that a randomly chosen student got either an 'A' or a 'B'?

Tip: When calculating probabilities from tables, always ensure you are clear on whether you're finding an unconditional or conditional probability.