youre playing a game where you defend your village from an orc invasion. there are 3 characters (elf…

youre 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 wont be a hobbit or use an umbrella?

youre 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 wont be a hobbit or use an umbrella?

Answer

Explanation:

Step1: Calculate total combinations

The total number of ways to choose a character and a tool is the product of the number of characters and the number of tools. So, $3\times5 = 15$ combinations.

Step2: Calculate number of non - desired combinations

The number of combinations with a hobbit is 5 (hobbit with each of the 5 tools). The number of combinations with an umbrella is 3 (each character with umbrella). But the combination of hobbit and umbrella is counted twice. So the number of non - desired combinations is $5 + 3-1=7$.

Step3: Calculate number of desired combinations

The number of desired combinations (not hobbit and not umbrella) is $15 - 7=8$.

Step4: Calculate probability

The probability $P$ is the number of desired combinations divided by the total number of combinations. So $P=\frac{8}{15}$.

Answer:

$\frac{8}{15}$