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. Find the value of y.

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 \( g - y = 25 - y \). The total number of students remaining in the hall becomes \( 28 + (25 - y) = 53 - y \).

According to the problem, the probability of selecting a girl at random after \( y \) girls leave the hall is given as \( \frac{3}{10} \).

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:

\[
\frac{25 - y}{53 - y} = \frac{3}{10}
\]

Now, we'll solve this equation for \( y \).

First, cross-multiply to get rid of the fraction:

\[
10(25 - y) = 3(53 - y)
\]

Expand both sides:

\[
250 - 10y = 159 - 3y
\]

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

\[
250 - 159 = 10y - 3y
\]

Simplify:

\[
91 = 7y
\]

Finally, solve for \( y \):

\[
y = \frac{91}{7} = 13
\]

So, \( y = 13 \).

**Conclusion:** 13 girls must leave the hall for the probability of selecting a girl at random to become 3/10.

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, 10 more boys enter the hall?
3. How would the problem change if the total number of students had been different?
4. What is the probability of selecting a boy after 13 girls leave the hall?
5. How does the probability change if only 5 girls leave the hall?
6. Can you set up a similar problem involving a different probability?
7. How would the answer change if the ratio of boys to girls had been different?
8. What if the probability of selecting a girl were \( \frac{1}{4} \) instead of \( \frac{3}{10} \)?

**Tip:** When dealing with probability problems, always make sure to relate the conditions given to an equation, then solve systematically for the unknown.

Explore a probability problem where the number of girls leaving a hall affects the probability of selecting a girl at random. Learn how to solve this problem step-by-step with detailed calculations and formulas. Suitable for Grades 10-12.

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