So an annoying question is floating around where four answers are given, asking the probability of picking the correct one, with the following answers provided:
I came up with a question to better visualize this and then I tried to solve that instead.
We have spheres of 3 colours. Red, Green and Blue.
There are 10 Red, 5 Green and 10 Blue spheres.
Assuming a colour is chosen at random, and then a sphere is chosen at random, what is the probability of picking the correct colour sphere?
The way I approach this is, we have a 1/3 chance of picking each colour and then either a 5/25 or 10/25 chance of picking the right sphere.
This gives me a probability of picking the right sphere 1/3 of the time. That does not make sense to me since there is a clear bias toward picking a Red or Green sphere. In fact, since the probabilities of picking a sphere always add up to one, changing the amount of spheres does not affect my answer at all. This further seems to indicate that my thought process is wrong. What is the correct way to approach this?