Question

Buffon's Needle Experiment A horizontal plane is

ruled with parallel lines 2 inches apart. A two-inch needle
is tossed randomly onto the plane. The probability that the
needle will touch a line is
P = 2／ (∫ sinθ dθ)
where
is the acute angle between the needle and any one of
the parallel lines. Find this probability.

Answer 1

To find the probability in Buffon's Needle Experiment, use the formula P = 2／ (∫ sinθ dθ) and evaluate the integral.

Step-by-step explanation:

To find the probability that the needle will touch a line in Buffon's Needle Experiment, we can use the formula P = 2／ (∫ sinθ dθ), where θ is the acute angle between the needle and any one of the parallel lines. Let's break down the steps:

1. Since the needle is tossed randomly, the acute angle θ can range from 0 to 90 degrees.
2. We need to integrate sinθ with respect to θ from 0 to 90 degrees.
3. By evaluating the integral, we can find the probability P.