Question

Sophia throws a dart at this square-shaped target:

Answer 1

Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)

Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)

Answer 2

if you assume that the dart always hits the target somewhere, then the chance of hitting the circle is the ratio of the area of the circle divided by the area of the square target.

any idea what the area of the circle is ?

Answer 3

not really, but im guessing its 3.14

Answer 4

there is a (famous) formula for the area of a circle. You have it in your notes

Answer 5

i do but i dont know where it is -.-

Answer 6

area of a circle = 3.14 * r^2 where r = radius

Answer 7

ok hold on let me solve it real quick

Answer 8

i just got this 2509.4

Answer 9

what did you get for r?
remember r = 1/2 the diameter of the circle ( which is given to be 3)

Answer 10

28.27..

Answer 11

i honstly do not know if im doing it right :/

Answer 12

1/2 of 3 = ?

Answer 13

1.5

Answer 14

right so
area of circle = 3.14 * 1.5^2

Answer 15

7.065

Answer 16

recall that 1.5^2 = 15 * 1.5

Answer 17

7.065 is correct

Answer 18

yay :D

Answer 19

Now the area of the big square = 9*9 = ?

Answer 20

81

Answer 21

ok
so required probability of hitting circle = 7.065 / 81

can you do that division?

Answer 22

0.0872

Answer 23

right?

Answer 24

yea
thats the answer to first part.

Answer 25

ok thx :)

Answer 26

and then it would be closer to 0 correct?

Answer 27

Part B is probability of hitting the white part which is a much greater area then the circle.
So will that be closer to 1 or 0?

Answer 28

In fact probabilty of hitting white part is 1 - 0.0872

Answer 29

- which is pretty close to 1.

Answer 30

0.9128 so it would be close to 1

Answer 31

yep

Answer 32

ok thx soooo much for your help :D

Answer 33

yw