Question

[7.05] Find the geometric probability of throwing a dart and hitting the yellow ring. You may assume the dart will not miss the target entirely.

Answer 1

What is the total area the guy can hit?

Answer 2

You know the radius, so you can determine what the total area of that dart-board is.

Answer 3

OK, so what is the radius of the dart-board?

Answer 4

11

Answer 5

Good, and what is the area of the dart-board then?

Answer 6

380.132

Answer 7

That's correct. Now do you know how you could determine the area of that yellow thingy?

Answer 8

treat it as one circle

Answer 9

radius 5

Answer 10

The yellow thingy is not a circle. You're partially correct :-)

Answer 11

OK, so if you notice, the yellow thingy is the circle of radius 5 (as you said), MINUS the red thingy.

Answer 12

And now if you find the area of that whole circle with radius 5, then subtract the area of that red circle with radius 2, you get the area of the yellow thingy.

Answer 13

I hope I'm not confusing you, but can you do it?

Answer 14

yah i got 65.97

Answer 15

65.97 for?

Answer 16

for the area of yellow portion

Answer 17

Yeah, that is correct, approximately. Good job!

Answer 18

All probabilities, including the geometric one, say this:\[{\rm Probability} = \dfrac{\mbox{Number of possible events we want}}{\mbox{Total number of possible events}}\]

Answer 19

We can treat the areas as "events." So you just divide the area of the yellow thingy by the total area.

Answer 20

And your geometric probability will turn out to be,\[P(\rm throw = yellow) \approx \dfrac{380.132}{65.97}\]

Answer 21

thanks

Answer 22

You're welcome!