A dart's spot along a meter ruler

Question

A dart is thrown at a 1-meter ruler and its landing spot is equally likely to be anywhere from 0 cm to 100 cm. So its position is uniform across the 100 cm length.

What is the probability that it lands between 65 cm and 100 cm?

Accepted Answer

For a position spread evenly along a length, the probability of hitting a target stretch equals that stretch's length divided by the whole length. P(	ext{event}) = \frac{	ext{length of favorable stretch}}{	ext{total length}}. The whole ruler is 100 cm. The favorable stretch, from 65 cm to 100 cm, is 100 - 65 = 35 cm long. So P(65 \le 	ext{spot} \le 100) = \frac{35}{100} = \frac{7}{20} = 0.35. A useful shortcut: "past the 65 cm mark" covers the final 35 cm of a 100 cm ruler, which is 35% by inspection, matching the calculation. Takeaway. For a uniform position on a length, probability is f…

A dart's spot along a meter ruler

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