If the needle in Problem 11 has length h . L, it’s possible for the needle to intersect morethan one line.(a) If L − 4, fnd the probability that a needle of length 7 will intersect at least one line.[Hint: Proceed as in Problem 11. Defne y as before; then the total set of possibilitiesfor the needle can be identifed with the same rectangular region 0 < y < L,0 < # < $. What portion of the rectangle corresponds to the needle intersecting aline?](b) If L − 4, fnd the probability that a needle of length 7 will intersect two lines.(c) If 2L , h < 3L, fnd a general formula for the probability that the needle intersectsthree lines.
If the needle in Problem 11 has length h . L, it’s possible for the needle to intersect morethan one line.(a) If L − 4, fnd the probability that a needle of length 7 will intersect at least one line.[Hint: Proceed as in Problem 11. Defne y as before; then the total set of possibilitiesfor the needle can be identifed with the same rectangular region 0 < y < L,0 < # < $. What portion of the rectangle corresponds to the needle intersecting aline?](b) If L − 4, fnd the probability that a needle of length 7 will intersect two lines.(c) If 2L , h < 3L, fnd a general formula for the probability that the needle intersectsthree lines.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
If the needle in Problem 11 has length h . L, it’s possible for the needle to intersect more
than one line.
(a) If L − 4, fnd the
[Hint: Proceed as in Problem 11. Defne y as before; then the total set of possibilities
for the needle can be identifed with the same rectangular region 0 < y < L,
0 < # < $. What portion of the rectangle corresponds to the needle intersecting a
line?]
(b) If L − 4, fnd the probability that a needle of length 7 will intersect two lines.
(c) If 2L , h < 3L, fnd a general formula for the probability that the needle intersects
three lines.
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