The number 52 is written as a sum of three natural numbers 52 = a + b + c (the triple (a, b, c) is ordered; e.g., the decompositions 52 = 14 + 15 +23 and 52 = 15+23+ 14 are different. Also, assume that all the decompositions have equal probability.) Given that there exists a triangle with sides a, b, and c, what is the probability that this triangle is isosceles?
The number 52 is written as a sum of three natural numbers 52 = a + b + c (the triple (a, b, c) is ordered; e.g., the decompositions 52 = 14 + 15 +23 and 52 = 15+23+ 14 are different. Also, assume that all the decompositions have equal probability.) Given that there exists a triangle with sides a, b, and c, what is the probability that this triangle is isosceles?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 46E
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![The number 52 is written as a sum of three natural numbers
52 = a +b+c
(the triple (a, b, c) is ordered; e.g., the decompositions 52 = 14 + 15 + 23 and 52 = 15 + 23 + 14 are different.
Also, assume that all the decompositions have equal probability.)
Given that there exists a triangle with sides a, b, and c, what is the probability that this triangle is isosceles?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc18ed615-e1a2-4562-ab9e-1d976a6e5a13%2Fbf975d13-1d38-4995-b847-51ec5d2d73f8%2Fzvpi6xr_processed.png&w=3840&q=75)
Transcribed Image Text:The number 52 is written as a sum of three natural numbers
52 = a +b+c
(the triple (a, b, c) is ordered; e.g., the decompositions 52 = 14 + 15 + 23 and 52 = 15 + 23 + 14 are different.
Also, assume that all the decompositions have equal probability.)
Given that there exists a triangle with sides a, b, and c, what is the probability that this triangle is isosceles?
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