In a class of 19 students, 6 are female and 10 have an A in the class. There are 7 students who are male and do not have an A in the class. What is the probability that a student who has an A is a male?

To solve this problem, we can use the principles of probability. Here's a step-by-step breakdown:

### Step 1: Define the variables
- **Total students (T):** 19
- **Female students (F):** 6
- **Students with an A (A):** 10
- **Male students without an A (M' ∩ A'):** 7

### Step 2: Determine the number of male students
Since the total number of students is 19 and there are 6 female students, the number of male students \( M \) is:
\[
M = T - F = 19 - 6 = 13
\]

### Step 3: Determine the number of male students with an A
We know that the number of male students who do not have an A is 7. Since there are 13 male students in total, the number of male students with an A \( M \cap A \) is:
\[
M \cap A = M - (M' \cap A') = 13 - 7 = 6
\]

### Step 4: Calculate the probability
We need to find the probability that a student who has an A is a male. This can be represented as:
\[
P(M \mid A) = \frac{P(M \cap A)}{P(A)}
\]
Where:
- \( P(M \cap A) \) is the number of male students with an A, which is 6.
- \( P(A) \) is the total number of students with an A, which is 10.

Substituting the values, we get:
\[
P(M \mid A) = \frac{6}{10} = \frac{3}{5} = 0.6
\]

### Final Answer
The probability that a student who has an A is a male is \( \boxed{0.6} \) or 60%.

Would you like more details or have any questions?

---

Here are some related questions:
1. What is the probability that a student selected at random is a female with an A?
2. What is the probability that a student who is male does not have an A?
3. How many students have neither an A nor are male?
4. What is the probability that a student selected at random is male?
5. How does the addition of one more female student with an A affect the probability?

**Tip:** When dealing with conditional probabilities, clearly identify the events and use the conditional probability formula \( P(B \mid A) = \frac{P(A \cap B)}{P(A)} \).

Understand how to calculate the probability that a student who has an A in a class of 19 students is male. This problem involves key concepts such as conditional probability, using the formula P(B|A) = P(A ∩ B) / P(A). Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation