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 won't be a hobbit or use an umbrella?

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Calculate Total Possible Outcomes: Total number of character choices is 3 and total number of tool choices is 5, so total possible outcomes are 3 * 5 = 15.Determine Unfavorable Outcomes: There is 1 hobbit character and 1 umbrella tool, so the unfavorable outcomes are choosing a hobbit with any tool (1 * 5 = 5) and choosing an umbrella with any character (1 * 3 = 3). But choosing a hobbit with an umbrella is counted twice, so we subtract that once (5 + 3 - 1 = 7).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, P(not hobbit or umbrella) = (15 - 7) / 15 = 8 / 15.

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