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

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

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

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Other answers:

How do I find the probability?
basically, you need the ratio between the square, and a circle that is subscribed in it.
lets define the side of a square using s.
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.
ok
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 `
are of a circle is A=pi r^2
ok
the probability that the point in the whole square that you randomly choose is \(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}\)
good luck....
if you have questions, you are always welcome to ask
There is no lengths or anything so im kinda confused
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)
there is length. length for what don't you see?
radius = s/2 side of the square = diameter of the circle = s
but i dont know the side of the square or diameter of the circle to figure it out. Sorry im lost
(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.)
So i make up a side length and a diameter of the circle?
Yes, that is what I showed
I denoted the length with letter s.
And now the probability of a randomly selected point, to lay on a circle is `A(circle) ÷ A(square)`
our area of the circle is πs²/4 area of the square is s²
still confused?
so 5^2=25 and 3.14*5^2 = 78 1/2
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.
i thought u said i do
We are just using any side-length "s" (regardless of what "s" is - of course, as long as s>0)
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.
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?
i know the formulas
ok, now divide the area of circle, by area of the square.
\(\displaystyle \LARGE {\rm P}=\frac{\rm A_{circle}}{\rm A_{square}}=\frac{\frac{\pi}{4}{\rm s}^2}{{\rm s}^2}=~...?\)
(the s² cancels on top and bottom, and you remain with ?)
pi/4?
3.14/4?
yes π/4 :)
(and again, that is regardless of the value of s, for all real values of s that are greater than 0)
okay
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
i did 3.14/4 = 157/200
ok so 157/250
|dw:1435286362761:dw|
An alternative is to think of the square with side length 2r so the radius of each circle is r |dw:1435286688332:dw|
ok
area of square = (2r)*(2r) = 4r^2 area of circle = pi*r^2 divide the area of the circle by the area of the square = pi*r^2/4r^2 = pi/4 either way you get the same answer
what do i put for r
r can be any number you want the 'r's will cancel, so it really doesn't matter
same with the 's's following SolomonZelman's method
so i could do 3.14*5^2/4*5^2?
yes, I guess to find the answer you can of course give the side of the square any length like 3.
I was just thinking that it asked for a complete prove that shows the probability of π/4 for all positive s.
or 3.14*5^2/4*2^2= 78 1/2 now what?
once you pick a number for r, you have to stick with it
and I should have used parenthesis (pi*r^2)/(4r^2)
so (3.14*5^2)/(4*5^2)?
= 157/200
now what?
what format do they want the answer? as a fraction? or decimal?
about 70% about 60% about 90% about 80%
oh ok
convert the fraction you have to a decimal then convert that decimal to a percent
0.785
convert 0.785 to a percent
78.5%
about 80%?
correct
well that was confusing lol thanku
whats a minor arc in a circle?
http://mathworld.wolfram.com/MinorArc.html any arc that is smaller than 180 degrees
an arc is just a piece of the whole circumference
ok so it be PS?
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that's one minor arc
MY CHOICES: PS, SO, SQ, PSR
the others didnt look right
yeah PS is the only minor arc SO isn't even an arc (it's a radius)
thats what i thought

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