Question

A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

Answer 1

about 70%
about 60%
about 90%
about 80%

Answer 2

@jim_thompson5910

Answer 3

How do I find the probability?

Answer 4

basically, you need the ratio between the square, and a circle that is subscribed in it.

Answer 5

lets define the side of a square using s.

Answer 6

The side of a the square is equivalent to the diameter of the circle.
The area of the square is just A=s². The area of the circle however is a little bit harder.

Answer 7

ok

Answer 8

The radius is s/2 (considering the fact that diameter =s)
Now, the formula for the area of the circle is `A=π • r²`

`A=π • (s/2)² = πs² /4 ` or alternatively `= (π/4) • s² `

Answer 9

are of a circle is A=pi r^2

Answer 10

ok

Answer 11

the probability that the point in the whole square that you randomly choose is

\(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}\)

Answer 12

good luck....

Answer 13

if you have questions, you are always welcome to ask

Answer 14

There is no lengths or anything so im kinda confused

Answer 15

that sentence is supposed to say
the probability that the point in the whole square that you randomly
`will lay on the shaded part ` choose is

(the part in gray I left out. apologize)

Answer 16

there is length. length for what don't you see?

Answer 17

radius = s/2
side of the square = diameter of the circle = s

Answer 18

but i dont know the side of the square or diameter of the circle to figure it out. Sorry im lost

Answer 19

(this probability that they ask you for, and that we will find, is true for any side length of the square, this is why the side of the square isn't given to us.)

Answer 20

So i make up a side length and a diameter of the circle?

Answer 21

Yes, that is what I showed

Answer 22

I denoted the length with letter s.

Answer 23

And now the probability of a randomly selected point, to lay on a circle is
`A(circle) ÷ A(square)`

Answer 24

our area of the circle is πs²/4
area of the square is s²

Answer 25

still confused?

Answer 26

so 5^2=25 and 3.14*5^2 = 78 1/2

Answer 27

no, you don't make up a length.
Not that it would matter, but you are not asked or meant to do this. I am sorry.

Answer 28

i thought u said i do

Answer 29

We are just using any side-length "s" (regardless of what "s" is - of course, as long as s>0)

Answer 30

I said that we use any sidelength 's'.
we show or work, for why is it so, that this probability is blank in this case?

if they wanted to, they would have given you the side. but they did not- for a reason.

Answer 31

But, do you understand my previous replies, how I found the area of a square and a circle in terms of s, or should I go over that again?

Answer 32

i know the formulas

Answer 33

ok, now divide the area of circle, by area of the square.

Answer 34

\(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}=\frac{\frac{\pi}{4}{\rm s}^2}{{\rm s}^2}=~...?\)

Answer 35

(the s² cancels on top and bottom, and you remain with ?)

Answer 36

pi/4?

Answer 37

3.14/4?

Answer 38

yes π/4 :)

Answer 39

(and again, that is regardless of the value of s, for all real values of s that are greater than 0)

Answer 40

okay

Answer 41

3.14/4
(if you use that approximation, then you might want to re-write the fraction, reduce it... or you know...)

i would perhaps go: 3.14/4= 314/500= 157/250

Answer 42

i did 3.14/4 = 157/200

Answer 43

ok so 157/250