Try this beautiful problem from Probability .You may use sequential hints to solve the problem.

## Probability | AMC-8, 2004 |Problem 22

At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is\(\frac{2}{5} \). What fraction of the people in the room are married men?

- \(\frac{3}{8}\)
- \(\frac{1}{2}\)
- \(\frac{1}{4}\)

**Key Concepts**

probability

combination

Number counting

## Check the Answer

But try the problem first…

Answer: \(\frac{3}{8}\)

AMC-8, 2007 problem 24

Challenges and Thrills in Pre College Mathematics

## Try with Hints

First hint

Find the married men in the room …

Can you now finish the problem ……….

Second Hint

Find the total people

can you finish the problem……..

Final Step

Assume that there are 10 women in the room, of which \(10 \times \frac{2}{5}\)=4 are single and 10-4=6 are married. Each married woman came with her husband,

so there are 6 married men in the room

Total man=10+6=16 people

Now The fraction of the people that are married men is \(\frac{6}{16}=\frac{3}{8}\)

## Other useful links

- https://www.cheenta.com/page-number-counting-amc-8-2010-problem-21/
- https://www.youtube.com/watch?v=YKtaNTxWA64