You're playing a game where you defend your village from an orc invasion. there are 333 characters (elf, hobbit, or human) and 555 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 won't be a hobbit or use an umbrella?

Answer with explanation:

→Number of characters in the game =3  (elf, hobbit, or human)

→Number of defense tools in the game =5 (magic, sword, shield, slingshot, or umbrella)

⇒Total number of elements in the set ,which consist of 3 characters and 5 defense tools = 3 × 5=15→→{(elf,magic),(elf,sword),(elf,shield),(elf,slingshot),(elf,umbrella),(Hobbit,magic),(Hobbit,sword),(Hobbit,shield),(Hobbit,slingshot),(Hobbit,Umbrella),(Human,magic),(Human,sword),(Human,shield),(Human,slingshot),(Human,Umbrella)}

→Out of 15 different ,pairs of Characters and tools,there are 7 pairs in which ,Hobbit as a character and umbrella as a defense tool is used. (Hobbit,magic),(Hobbit,sword),(Hobbit,shield),(Hobbit,slingshot),(Hobbit,Umbrella), (Human,Umbrella), (elf,umbrella).

Then, required probability

your answer would be 10x - 1