Try this beautiful problem from Probability.

## Problem based on Probability | AMC-8, 2016 | Problem 21

A box contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?

- \(\frac{3}{5}\)
- \(\frac{2}{5}\)
- \(\frac{1}{4}\)

**Key Concepts**

probability

combination

fraction

## Check the Answer

But try the problem first…

Answer: \(\frac{2}{5}\)

AMC-8, 2016 problem 21

Challenges and Thrills in Pre College Mathematics

## Try with Hints

First hint

There are 5 Chips, 3 red and 2 green

Can you now finish the problem ……….

Second Hint

We draw the chips boxes in such a way that we do not stop when the last chip of color is drawn. one at a time without replacement

Can you finish the problem……..

Final Step

There are 5 Chips, 3 red and 2 green

we draw the chips boxes in such a way that we do not stop when the last chip of color is drawn.

if we draw all the green chip boxes then the last box be red or if we draw all red boxes then the last box be green

but we draw randomly. there are 3 red boxes and 2 green boxes

Therefore the probability that the 3 reds are drawn=\(\frac{2}{5}\)

## Other useful links

- https://www.cheenta.com/largest-and-smallest-numbers-amc-8-2006-problem-22/
- https://www.youtube.com/watch?v=_HYhADRACPs

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