You're playing a game where you defend your village for me or evasion there are three characters of habit or human and five defensive tools magic sword shield slingshot or umbrella to pick from if you randomly choose your character into what is your probability that you won't be a hobby or use an umbrella

Answers

Answer 1

Answer:

[tex]P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{14}{15}[/tex]

Step-by-step explanation:

Your question is poorly formatted (See comment section for complete question)

Given

[tex]x = \{elf, hobbit, human\}[/tex] ---- characters

[tex]n(x) =3[/tex]

[tex]y = \{Magic,Sword,Shield,Slingshot,Umbrella\}[/tex] --- tools

[tex]n(y) = 5[/tex]

Required

The probability that your character won't be a hobbit or your tool won't be an umbrella?

First we calculate the probability of choosing a hobbit.

[tex]x = \{elf, hobbit, human\}[/tex]

[tex]n(hobbit) = 1[/tex]

So:

[tex]P(hobit) = \frac{n(hobbit)}{n(x)}[/tex]

[tex]P(hobit) = \frac{1}{3}[/tex]

Using the complement rule, we calculate the probability of not choosing a hobbit

[tex]P(Not\ hobbit) = 1 - P(hobbit)[/tex]

[tex]P(Not\ hobbit) = 1 - \frac{1}{3}[/tex]

[tex]P(Not\ hobbit) =\frac{2}{3}[/tex]

Next, we calculate the probability of choosing an umbrella.

[tex]y = \{Magic,Sword,Shield,Slingshot,Umbrella\}[/tex]

[tex]n(Umbrella) = 1[/tex]

So:

[tex]P(Umbrella) = \frac{n(Umbrella)}{n(y)}[/tex]

[tex]P(Umbrella) = \frac{1}{5}[/tex]

Using the complement rule, we calculate the probability of not choosing an umbrella

[tex]P(Not\ Umbrella) = 1 - \P(Umbrella)[/tex]

[tex]P(Not\ Umbrella) = 1 - \frac{1}{5}[/tex]

[tex]P(Not\ Umbrella) = \frac{4}{5}[/tex]

The required probability is calculated using:

[tex]P(A\ or\ B) = P(A) + P(B) - P(A)P(B)[/tex]

In this case;

[tex]P(Not\ hobbit\ or\ Not\ Umbrella) = P(Not\ hobbit) + P(Not\ Umbrella) -[/tex] [tex]P(Not\ hobbit)*P(Not\ Umbrella)[/tex]

[tex]P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{2}{3} + \frac{4}{5} - \frac{2}{3} * \frac{4}{5}[/tex]

[tex]P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{2}{3} + \frac{4}{5} - \frac{8}{15}[/tex]

Take LCM

[tex]P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{10+12-8}{15}[/tex]

[tex]P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{14}{15}[/tex]


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If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

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Answers

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Step-by-step explanation:

Let be [tex]A(x,y) = (-10, 8)[/tex] on the terminal side of an angle in standard position and let be [tex]O(x,y)[/tex] the origin of the angle and the origin of the Cartesian plane. By definition of tangent, we make use of the following expression:

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[tex]y_{A}, y_{O}[/tex] - y-Coordinates of point A and point O.

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