There are 28 boys and 25 girls in a school hall. After y girls leave the hall, the probability of selecting a girl at random becomes 3/7. Find the value of 

Let's denote the initial number of boys as \( b = 28 \) and the initial number of girls as \( g = 25 \).

After \( y \) girls leave the hall, the number of girls remaining is \( 25 - y \). The total number of students remaining in the hall becomes \( 28 + (25 - y) = 53 - y \).

The problem states that the probability of selecting a girl at random after \( y \) girls leave the hall is \( \frac{3}{7} \).

This probability can be written as:

\[
\frac{\text{Number of girls remaining}}{\text{Total number of students remaining}} = \frac{25 - y}{53 - y}
\]

So, we have:

\[
\frac{25 - y}{53 - y} = \frac{3}{7}
\]

Now, let's solve this equation for \( y \).

First, cross-multiply to eliminate the fraction:

\[
7(25 - y) = 3(53 - y)
\]

Expand both sides:

\[
175 - 7y = 159 - 3y
\]

Now, bring all the \( y \)-terms to one side and the constants to the other side:

\[
175 - 159 = 7y - 3y
\]

Simplify:

\[
16 = 4y
\]

Finally, solve for \( y \):

\[
y = \frac{16}{4} = 4
\]

**Conclusion:** \( y = 4 \). So, 4 girls must leave the hall for the probability of selecting a girl at random to become \( \frac{3}{7} \).

Do you want more details or have any questions?

Here are some related questions:

1. What is the probability of selecting a girl before any girls leave?
2. What if instead of girls leaving, 7 more boys enter the hall?
3. How would the problem change if the probability was \( \frac{2}{5} \) instead of \( \frac{3}{7} \)?
4. What is the probability of selecting a boy after 4 girls leave the hall?
5. How does the probability change if only 2 girls leave the hall?
6. Can you create a similar problem involving a different probability?
7. How would the answer change if there were 30 boys instead of 28?
8. What if the probability of selecting a girl were \( \frac{4}{7} \) instead of \( \frac{3}{7} \)?

**Tip:** When solving problems involving probability, always carefully set up the equation based on the given information and then solve step by step.

Explore a probability problem involving adjusting the number of girls in a school hall to achieve a probability of selecting a girl at random as 3/7. Learn how to solve equations and use fractions to determine the number of girls that need to leave the hall. Suitable for Grades 7-9.

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