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

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

AMC-8, 2007 problem 24

Challenges and Thrills in Pre College Mathematics

## Try with Hints

Find the married men in the room …

Can you now finish the problem ……….

Find the total people

can you finish the problem……..

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