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You're playing a game where you defend your village from an orc invasion. There are characters (elf, hobbit, or human) and 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?
Full solution
Q. You're playing a game where you defend your village from an orc invasion. There are characters (elf, hobbit, or human) and 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?
- Calculate Total Possible Outcomes: Total number of character choices is and total number of tool choices is , so total possible outcomes are .
- Determine Unfavorable Outcomes: There is hobbit character and umbrella tool, so the unfavorable outcomes are choosing a hobbit with any tool () and choosing an umbrella with any character (). But choosing a hobbit with an umbrella is counted twice, so we subtract that once ().
- Calculate Probability: The probability of not being a hobbit or using an umbrella is the total possible outcomes minus the unfavorable outcomes, divided by the total possible outcomes. So, .
