Probability Problem

  • Thread starter LLS
  • Start date
  • #1
LLS
40
0

Homework Statement


On a game show, darts are thrown at a circular target. It's radius = 10 meters. Within the target is another circular region called the red zone. If a dart is thrown and hits the red zone, the player gets 25 bonus points. The radius of the red zone = 5 meters. If every dart thrown hits the target at a random point, what is the probability that a dart hits the red zone?

Homework Equations



?

The Attempt at a Solution


My answer is 1/2 or a 50% chance of hitting the red zone.
The inner circle takes up half the space of the bigger one.
 

Answers and Replies

  • #2
kenewbie
239
0
My answer is 1/2 or a 50% chance of hitting the red zone.
The inner circle takes up half the space of the bigger one.

Does it? The radius of the red zone is half the radius of the entire disk. Is this the same as occupying half the space? Try to calculate the area of both and you'll find out.

k
 
  • #3
LLS
40
0
Does it? The radius of the red zone is half the radius of the entire disk. Is this the same as occupying half the space? Try to calculate the area of both and you'll find out.

k

The answer should be 1/4 or 25%?

Thank you
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
43,021
970
You don't have a good answer until you understand it- and then you don't have to ask if it is right!
It is the point hit that is "random"- which, here, means all points are equally likely to be hit. Is it points in an area or on a line that are equally likely? So which caculation should you use?
 
  • #5
LLS
40
0
You don't have a good answer until you understand it- and then you don't have to ask if it is right!
It is the point hit that is "random"- which, here, means all points are equally likely to be hit. Is it points in an area or on a line that are equally likely? So which caculation should you use?

The area of the big circle = 100 x pi
The area of the smaller circle = 25 x pi

There's 4 times the area in the big circle.
Wouldn't that mean that you are 4 times more likely to hit the big area?
The chance would be 1/4.
 

Suggested for: Probability Problem

  • Last Post
Replies
15
Views
281
  • Last Post
Replies
0
Views
2
Replies
15
Views
323
  • Last Post
Replies
34
Views
3K
Replies
2
Views
442
  • Last Post
Replies
22
Views
750
Replies
2
Views
247
  • Last Post
Replies
6
Views
665
Replies
9
Views
292
  • Last Post
Replies
12
Views
1K
Top