You play darts with a friend. The board is a circle with a 6-inch radius. The "Bull's Eye" is a smaller circle in the center of the board with an 0.25-inch radius. You throw darts (small metal arrows) at the board. At the end of six weeks, she has thrown 500 darts. She hit the board every time and hit the Bull's Eye 1 time If you throw 500 darts, how many times should you expect to hit the Bull's Eye by random chance? Compare this result to your friend's result. Is she a skilled player for hitting the bull's eye or is the result of hers expected?

Question

Johns

Mathematics

20 June, 02:22

You play darts with a friend. The board is a circle with a 6-inch radius. The "Bull's Eye" is a smaller circle in the center of the board with an 0.25-inch radius. You throw darts (small metal arrows) at the board. At the end of six weeks, she has thrown 500 darts. She hit the board every time and hit the Bull's Eye 1 time If you throw 500 darts, how many times should you expect to hit the Bull's Eye by random chance? Compare this result to your friend's result. Is she a skilled player for hitting the bull's eye or is the result of hers expected?

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Kaufman · Answer 1

The area of the board = πr² = 36 π square inches

Area of the Bull's eyes = πr² = 0.0625 π square inches

If a dart is thrown at random, the probability that it will hit the bull's eye can be calculated as:

Area of Bulls's Eyes divided by Area of Complete Board

So, probability of hitting the bulls'e eye = 1/576 = 0.001736

The friend hit Bull's eye once in a 500 throws. So the probability of hitting the Bull's eyes will be = 1/500 = 0.002

If we compare the two probabilities, they are close to each other. So we can conclude that the friend is not a skilled player and she hit the bull's eye just by chance.