Geometric Probability that asteroid will hit the earth

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About once a year, an asteroid enters the solar system in the region between the sun and the orbit of the planet Mars. What is the geometric probability that it will hit the earth? The distance from the sun to Mars is 142 million miles. The diameter of the earth is 7927 miles, and the diameter of the sun is 864,400 miles.

Using the formula for area of a circle, I found the area of the entire circle from the center of the sun to Mars. Then I subtracted the area of the sun, calculated the area of the earth, and set up a ratio... but came nowhere near the answer on the answer, which is 7.7436x10-10 or 7.7908x10-10. Where did I go wrong?
 
interval said:
About once a year, an asteroid enters the solar system in the region between the sun and the orbit of the planet Mars. What is the geometric probability that it will hit the earth? The distance from the sun to Mars is 142 million miles. The diameter of the earth is 7927 miles, and the diameter of the sun is 864,400 miles.

Using the formula for area of a circle, I found the area of the entire circle from the center of the sun to Mars. Then I subtracted the area of the sun, calculated the area of the earth, and set up a ratio... but came nowhere near the answer on the answer, which is 7.7436x10-10 or 7.7908x10-10. Where did I go wrong?
Click to expand...
Check your calculations. I got the second answer. The sun's area is too small to have much effect on the answer.
 
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