Question

What is the probability that a randomly chosen point lies in the shaded region? (leave the answer as a fraction and leave pi in your answer)

Answer 1

area of shaded region divided by total area

Answer 2

the triangle is shaded

Answer 3

ok so the area of the circle is easy enough right? since the radius is 5 the area is \(\pi\times 5^2=25\pi\)

Answer 4

Yes, I have that so far.

Answer 5

and you have two triangles both with base 5 and height 5 so the total area of the two triangles is
\(5\times 5=25\)

Answer 6

take the ratio to get your answer

Answer 7

So then isn't it just one..

Answer 8

oh no the areas are not the same

Answer 9

your shaded region has area 25, total circle has area \(25\pi\)

Answer 10

oh wait never mind... so it's 25pi over 25?

Answer 11

no other way around
shaded area over total area

Answer 12

so 25 over 25pi?

Answer 13

don't forget probability is a number between 0 and 1
right
cancel the 25

Answer 14

1pi? hahha

Answer 15

\(\frac{25}{25\pi}=\frac{1}{\pi}\)

Answer 16

not \(1\pi\) but rather \(\frac{1}{\pi}\)

Answer 17

Okay thank you!

Answer 18

yw