Chapter 4.4, Problem 61E

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

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 π ∫ 0 π / 2 sin θ d θ where θ is the acute angle between the needle and any one of the parallel lines. Find this probability.

To determine

To calculate: The value of probability, P=2π0π2sinθdθ

Explanation

Given:

The needle falls according to the diagram

The probability that it will touch a line is P=2Ï€âˆ«0Ï€2sinÎ¸dÎ¸.

Formula used:

The probability can be solved by integrating the function within the limits according to formula

âˆ«absinx=[âˆ’cosx]ab

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