A test was given to a group of students. The grades and gender are summarized below



A

B

C

Total

Male

5

14

6

25

Female

11

16

4

31

Total

16

30

10

56


If one student is chosen at random from those who took the test,

Find the probability that the student got a 'C' GIVEN they are female.

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.

A test was given to a group of students. The grades and gender are summarized below.

A
B
C
Total
Male
5
14
6
25
Female
11
16
4
31
Total
16
30
10
56

If one student is chosen at random from those who took the test, find the probability that the student got a 'C' GIVEN they are female.

Learn how to calculate the conditional probability of a student getting a 'C' given they are female using real test data. This problem involves key concepts of probability and conditional probability, with step-by-step breakdowns. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation