Question

There are 3 pink, 3 violet, 4 yellow, and 2 brown marbles in a hat. you pick 2 marbles from the hat. marbles are not returned after they have been drawn. find the probability that the first marble is violet and the second marble is pink.

Answer 1

First, we add everything together, so; 3 + 3 + 4 + 2 = 12. This means every marble has a 8.33% chance of being chosen, however since there are more than others we add those separate percentages together. 

Pink: 25%
Violet: 25%
Yellow: 33.33%
Brown: 16.66%
These are the chances of you getting either color. Since the problem asks what is the probability of finding a violet marble,we just look at the written percentages to see we have a 25% chance of choosing a violet marble.

The next step is to see what is the probability of choosing a pink marble, except we have to change things up a bit. Since we removed 1 marble, that changes ALL the percentages again, so we must rewrite the percentages. 12 - 1 is easily solved as 11, and so this means every marble has a 9.0909091% of being chosen. Let's rewrite the grouped percentages now:

Pink: 27.27%
Violet: 18.18%
Yellow: 36.36%
Brown: 18.18%

Now we see that with one marble removed, and that marble not being pink, we have a 27.27% chance of picking a pink marble.

Your Answer: 25% of Violet first time, 27.27% of Pink second time.

(How To Get Percentages?): Simple, you divide 100 (since whatever number we start out with as long as it claims nothing is missing equal 100%) by whatever number of objects you have. So as an example, if I have 5 objects, 100 / 5 = 20. This means every individual object has a 20% chance of being chosen. But we then arrange everything into whatever groups (in your problems case, colors) and multiply by the amount. So say I have 3 green balls and 2 white balls, 3 x 20 = 60 and 2 x 20 = 40 so I have a 60% of getting a green ball and 40% chance of a white ball.

Hope this helps and I hope even more you learned something :D