Question: Target

Comment on Target

so do we always use this method to solve such questions?
area of smaller/area of larger circle?

gmat-admin's picture

Yes, we can use the same approach for similar questions involving probability and areas.

For the denominator why didn't you subtract the area of smaller circle from larger circle to get the actual area of larger circle without repetition.
gmat-admin's picture

The denominator is for the total number of possible outcomes.

We're randomly selecting a point inside the larger circle, so the possible outcomes include points that are inside the smaller circle AND points that are in the doughnut shaped part around the smaller circle (i.e., outside the smaller circle).

So, if we exclude the points inside the smaller circle (as you suggest), then we're not considering all possible outcomes.

Does that help?

Cheers,
Brent

Brent, why couldnt we use this as the denominator?

Area of small circle + area of donut shaped part = Pi * 4 + Pi* 9 = Pi * 13?

thanks
gmat-admin's picture

It looks like you're taking the radius of the OUTER circle (radius 5) - and subtracting the radius of the INNER circle (radius 2) to get 3.
So, the donut has a THICKNESS (aka width) of 3.
That part is correct.

However, we cannot say that the area of the donut (with a thickness of 3) will be the same as the area of a circle with radius 3.

If you want to see why, consider the same question, but make the INNER circle have radius 100, and make the OUTER circle have radius 101.
So, we have a very big DONUT with a thickness of 1.
The area of this big donut will be MUCH greater than the area of one CIRCLE with radius 1.

Does that help?

Cheers,
Brent

Hi Brent,

Please correct me if my approach is wrong below:

I used the AND formula to write P(Point in Large circle AND point in small circle) = 1*4pi/25pi

1 because its certain that the point is on the Large Circle and 4pi/25pi because thats the probability that the point is on the small circle, concluding with the same answer. Just wanted to check because I don't want to go wrong with similar questions later! Thanks!
gmat-admin's picture

That approach is perfectly valid.

That said, we're already told that the point is selected from the region inside the larger circle.
So, it isn't really necessary for our solution to make sure the point is inside the larger circle.
That said, it doesn't change the outcome.
So, either way works.

Cheers,
Brent

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