Probability of Hitting Red Zone on Game Show Darts Target

[LLS]

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

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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.

 

[kenewbie]

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

 

[LLS]

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

 

[HallsofIvy]

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?

 

[LLS]

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.