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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?

You're playing a game where you defend your village from an orc invasion. There are 33 characters (elf, hobbit, or human) and 55 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.\newlineIf you randomly choose your character and tool, what is the probability that you'll be a magic elf?

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Full solution

Q. You're playing a game where you defend your village from an orc invasion. There are 33 characters (elf, hobbit, or human) and 55 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.\newlineIf you randomly choose your character and tool, what is the probability that you'll be a magic elf?
  1. Character and Tool Choices: Total number of character choices = 33 (elf, hobbit, human)\newlineTotal number of defense tool choices = 55 (magic, sword, shield, slingshot, umbrella)\newlineTo find the total number of combinations, multiply the number of character choices by the number of tool choices.\newlineTotal combinations = 3×5=153 \times 5 = 15
  2. Favorable Outcome Calculation: Only one combination makes you a magic elf. So, the number of favorable outcomes =1= 1
  3. Probability Calculation: Probability ( extit{P}) of being a magic elf = Number of favorable outcomes / Total combinations\newlineP(magic elf)=115P(\text{magic elf}) = \frac{1}{15}

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