Question

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 $$ P=\frac{2}{\pi} \int_{0}^{\pi / 2} \sin \theta d \theta $$ where $\theta$ is the acute angle between the needle and any one of the parallel lines. Find this probability.

          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
$$
P=\frac{2}{\pi} \int_{0}^{\pi / 2} \sin \theta d \theta
$$
where $\theta$ is the acute angle between the needle and any one of the parallel lines. Find this probability.

Added by Virginia W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

12/07/2022

Step 1

Step 1:** The probability that the needle will touch a line is given by the formula: $$ P = \frac{2}{\pi} \int_{0}^{\frac{\pi}{2}} \sin \theta d \theta $$ ** Show more…

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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 $$ P=\frac{2}{\pi} \int_{0}^{\pi / 2} \sin \theta d \theta $$ where $\theta$ is the acute angle between the needle and any one of the parallel lines. Find this probability.