Statistics - Probability Misunderstanding

I have a misunderstanding about when you times a probability by two - here's an example.
Here is one question:
A bag contains 30 red discs and 20 blue discs. A second bag contains 15 red discs and 35 blue discs A disc is drawn at random from each bag. Find the probability that these two discs are of different colours.

The answer is
0.4*15/50 + 0.6*35/50 = 0.54

Without looking at the mark scheme, I would have thought to times each of those seperate bold sections by two to represent how they could be picked in any order. I'm clearly incorrect so can anyone explain why?

Reply 1

Xzerzes

I'm pretty sure what you have written is correct. You need to times the opposites to find the probabilities of the combinations which meet the criteria which in this case is to either get RB or BR so the probability is the two added together
BR= 20/50 * 15/50
RB= 30/50 * 35/50
Alternatively you could also do 1-(BB+RR) and if you get the same number you'll know you're right