Question

The state of Connecticut is approximated by a rectangle 100 mi by 50 mi.

Hartford is approximately at the center of Connecticut. If a meteor hit the
earth within 200 mi of Hartford, find the probability that the meteor landed in
Connecticut.

Answer 1

4.0%

Explanation:

If we assume that potential impact sites are uniformly distributed over the area, the probability of interest is the ratio of the area of Connecticut to the area of the circle within 200 miles of Hartford.

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area of circle

The area of a circle with radius 200 miles is ...

A = πr²

A = π(200 mi)² = 40000π mi² ≈ 125,664 mi²

area of CT

The area of a rectangle 100 miles by 50 miles is ...

A = LW

A = (100 mi)(50 mi) = 5000 mi²

probability

The probability of interest is the ratio of these areas:

p(impact in CT) = (5000 mi²)/(125664 mi²) ≈ 0.03979

The probability the meteor landed in Connecticut is about 4.0%.