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# A stick of length L is to be broken into three parts

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Manager
Joined: 20 Aug 2017
Posts: 104
A stick of length L is to be broken into three parts  [#permalink]

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25 Dec 2019, 02:45
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Difficulty:

75% (hard)

Question Stats:

21% (01:19) correct 79% (01:13) wrong based on 33 sessions

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Q. A stick of length L is to be broken into three parts. What is the probability that the resulting pieces form a triangle?

A) $$\frac{1}{2}$$
B) $$\frac{1}{3}$$
C) $$\frac{1}{4}$$
D) $$1$$
E) None of these.
VP
Joined: 19 Oct 2018
Posts: 1306
Location: India
Re: A stick of length L is to be broken into three parts  [#permalink]

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25 Dec 2019, 06:09
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Good Question!!

Suppose length of 3 parts is x, y and z

x≤y≤z

Minimum length z can have is L/3. (when x=y=z)

Maximum length of z is infinitesimally smaller than L/2. (As x+y>z)

Probability= (0.5L-0.33L)/(L-0.33L) = 1/4

uchihaitachi wrote:
Q. A stick of length L is to be broken into three parts. What is the probability that the resulting pieces form a triangle?

A) $$\frac{1}{2}$$
B) $$\frac{1}{3}$$
C) $$\frac{1}{4}$$
D) $$1$$
E) None of these.
Intern
Joined: 01 Jan 2019
Posts: 2
Re: A stick of length L is to be broken into three parts  [#permalink]

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18 Jan 2020, 11:57
I tried finding the probability of not making a triangle.

B1 = probability the first break doesn't give a triangle
B2 = probability the second break doesn't give a triangle

Then we want:

1-B1*B2

I'd say B1=1, no matter where we make the first break, we can potentially have an impossible triangle.

B2=1/2 ... the condition for the second break to make an impossible triangle would be that it leave an unbroken length of L/2. This means the second break can be made in a length of L/2.

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Re: A stick of length L is to be broken into three parts   [#permalink] 18 Jan 2020, 11:57
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