In a bag of keys, there are 13 silver keys, 6 black keys, 11 copper keys, and 2 painted keys of various colors. One key is drawn out at random. What is the probability that the key that is drawn is silver or copper?

The best thing to do here is to put each of these into fractions, with the total (31) as the denominator.

14/31= silver

6/31= black

8/31= copper

3/31= various colours.

As you're looking for the keys that are silver or copper, you've got to add the two denominators together, which gives you 14+8= 22.

This cannot be simplified further, therefore, the probability of choosing either a silver or copper key is 22/31

Hope this helps :)

linear pair postulates