Question

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

Answer 1

probability that the point will be in the shaded region=area of shaded region / total area

Answer 2

But I don't have any numbers to work with :p

Answer 3

well actully u dont need any numbers
let the side of square =a

Answer 4

Ok

Answer 5

calculate the areas in terms of a

Answer 6

Can you give an example?

Answer 7

Not getting it :p

Answer 8

ok
area of square=a^2
is that right

Answer 9

Yeah, and then what do I do with the outside parts?

Answer 10

u have 4 semi-circles out there
now u tell me what is the radius of the each semi-circle?

Answer 11

1/2 a

Answer 12

exactly

Answer 13

area of 4 semi-circles equals to 2 circles
am i right?

Answer 14

yep

Answer 15

now u can calculate the area of shaded region in terms of a : 2 circles with radius a/2

Answer 16

Now how do I get a percentage from that?

Answer 17

area of shaded region will be a term like A a^2
total area will be a term like B a^2
then
probability=(A a^2)/(B a^2)=A/B

Answer 18

the answer is
\[\frac{\pi}{\pi+2}\]
if u wanna check