Question

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 1

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

         $=\frac{\text{Total favorable outcome}}{\text{Total Possible outcome}}\\\\=\frac{15-7}{15}=\frac{8}{15}$      

Answer 2

The probability of the Hobbit not using an umbrella is

$\dfrac{14}{15}$

Probability

Probability is the ratio of favorable events to a total number of events.

Given

The number of characters is = 3 (elf, hobbit, or human)

The number of defense tools = 5  (magic, sword, shield, slingshot, or umbrella)

The total number of combinations = 5*3 = 15

Probability is given by a formula

$\rm P(favorable\ events) =\dfrac{Favorable\ event}{Total\ nunber\ of\ events}$

How to calculate probability?

Probability of hobbit use umbrella

$\rm P(Hobbit\ use\ umbrella)= \dfrac{Hobbit\ use\ umbrella}{Total\ number\ of\ events}$

$\rm P(hobbit\ use\ umbrella) = \dfrac{1}{15}$

So

The probability of not  hobbit using an umbrella will be

$\rm P( Hobbit\ use\ umbrella) + P( Hobbit\ not\ use\ umbrella)=1$

$\rm P( Hobbit\ not\ use\ umbrella)=1- P( Hobbit\ use\ umbrella)$

$\rm P( Hobbit\ not\ use\ umbrella)=1-\dfrac{1}{15}$

$\rm P( Hobbit\ not\ use\ umbrella)=\dfrac{14}{15}$

Thus, the probability of the Hobbit not using an umbrella is

$\dfrac{14}{15}$

To know more about the probability link is given below.

https://brainly.com/question/795909