Question

Plz help

Wendy throws a dart at this square-shaped target:

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

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

Answer 1

what do you think?

Answer 2

ummm for part a 0?

Answer 3

true and the opposite for part b

Answer 4

ok

Answer 5

here we have to compute the area of the black circle

Answer 6

furthermore, we have to compute the area of the white square

Answer 7

ok

Answer 8

what is the area of the white square?

Answer 9

100

Answer 10

ok!

Answer 11

what is the area of the black circle?
hint:
you can use this value \[\pi = 3.14\]

Answer 12

I don't know what the radius is

Answer 13

the radius is half-diamter, so:
radius = 2/2=...?

Answer 14

1

Answer 15

ok!

Answer 16

so what is the area of the circle?

Answer 17

it's 3.14

Answer 18

hint:
\[area = \pi \times {\left( {radius} \right)^2}\]

Answer 19

ok!

Answer 20

now, the requested probability in part A, is given by the subsequent ratio:
\[\large p = \frac{{area\;of\;the\;circle}}{{area\;of\;the\;square}} = ...?\]

Answer 21

since the favorable cases are given by the area of the black circle, whereas the possible cases are given by the area of the white square

Answer 22

0.0314

Answer 23

ok! We can write that probability in percentage form, so we have:
p= 3.14 %

Answer 24

ok

Answer 25

Now, what is the difference between the area of the square and the area of the circle? Namely what is:
100-3.14=...?

Answer 26

96.86

Answer 27

ok! For the part A, we can say that the probability is closer to 0, since 0.0314 is closer to zero

Answer 28

ok

Answer 29

Finally, the requested probability in part B, is given by the subsequent formula:
\[p = \frac{{area\;of\;the\;square - area\;of\;the\;circle}}{{area\;of\;the\;square}} = ...?\]

Answer 30

since, the favorable cases are given by the difference between those areas, whereas the possible cases are given by the area of the square

Answer 31

\[\Large \begin{gathered}
p = \frac{{area\;of\;the\;square - area\;of\;the\;circle}}{{area\;of\;the\;square}} = \hfill \\
\\
= \frac{{96.86}}{{100}} = ...? \hfill \\
\end{gathered} \]

Answer 32

0.9686

Answer 33

ok!, that probability is closer to 1. Furthermore it can be rewritten as below:
p= 96.86%

Answer 34

ok that's it right?

Answer 35

yes!