There are only red , blue and purple counters in a bag. The ratio of the number of red counters to the number of blue counters is 3 : 17. If a counter is taken randomly the probability that it is purple is 0.2 Work out the probability for it to be red.

I would first take into account all the variables - there are red, blue and purple counters, we know the ratio of red to blue and we know the probability of purple is 0.2.
As I know the probability that purple being picked is 20% or 0.2, I would explain that as a first step, I would acknowledge that that suggests that purple counters make up 20% of the total counters in the bag. Next, as there are only red, blue and purple, this suggests that red and blue combined make up (100% of the whole bag - 20% purple = ) 80% of the bag. I can then calculate the probability of each based on the ratio by multiplying up to the total percentage.
I would take the total of the two parts of the ratio (20 as 17+ 3 =20) and multiply it to the percentage that it makes up, so in this case I would multiply both sides of the ratio by 4, giving me 12:68 counters for red:blue. Multiplying up to the total percentage would also give me their percentage shares, so I would have a 68% chance of picking a blue counter, 20% chance of a purple one and finally a 12% chance of a red counter, giving me my answer.