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:
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
The equation to model this would be 65 = 11r + 9s.
In this equation, we know that the total number he works is 65. We also know he burns 11 every time he runs for an hour. Therefore we can multiply 11 by r. We also know he burns 9 for every hour he spends swimming. Therefore we can multiply 9 by s.
When we put all three of these things together, we get 65 = 11r + 9s.
