Circle probability

**jarny** · January 31st 2007, 04:55 PM

Five concentric circles with radii 1, 2, 3, 4, and 5 are drawn, one inside the other, dividing the circle of radius 5 into five regions: a circle of radius and 4 annuli (rings). What is the probability that a point chosen randomly from within the circle of radius 5 lies in the annulus whose inner radius is 3 and whose outer radius is 4? Can someone tell me if this is the right answer? i got a 7/25 chance. THanks!

**Soroban** · January 31st 2007, 05:10 PM

Hello, jarny!

You're correct . . . Nice work!

**mmathh** · October 23rd 2011, 02:21 PM

How? could you explain. i need help with the same question. thank you.

**Soroban** · October 23rd 2011, 02:55 PM

Hello, mmathh!

Five concentric circles with radii 1, 2, 3, 4, and 5 are drawn, one inside the other,
dividing the circle of radius 5 into five regions: a circle of radius 1 and 4 annuli (rings).

What is the probability that a point chosen randomly from within the circle of radius 5
lies in That Ring whose inner radius is 3 and whose outer radius is 4?

The total area is: . $A \:=\:\pi r^2 \:=\:\pi(5^2) \:=\:25\pi$

The circle with radius 4 has area: . $\pi (4^2) \,=\,16\pi$
The circle with radius 3 has area: . $\pi(3^2) \,=\,9\pi$

The area of That Ring is: . $16\pi - 9\pi \,=\,7\pi$

Therefore: . $P(\text{point is in That Ring}) \:=\:\frac{7\pi}{25\pi} \:=\:\frac{7}{25}$

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