Probabilities of compound events

Question

You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. If you randomly choose your character and tool, what is the probability that you'll be a magic elf?

Answer 1

The probability of selecting elf is 1/3. Once you pick elf, you now pick the defense tool. The probability of selecting magic is 1/5. Therefore, the probability of selecting magic elf is 1/3•1/5 = 1/15

A tree diagram might help: