# 7 cm long stick cut in three pieces . length of each pieces are natural number. what is the probability of formating triangle from

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7 cm long stick cut in three pieces . length of each pieces are natural number. what is the probability of formating triangle from the three pieces of the stick .please write in details ​

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1. Question:

The 7 cm long stick cut in three pieces, length of each pieces are natural number. What is the probability of formating triangle from the three pieces of the stick.

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Solution:

Let, three pieces be a, b and c.

We know, a + b + c = 7 and a, b & c € N

Let [ ] represent a piece.

Number of ways possible for a + b + c = 7,

Here arranged doesn’t matter it means

» (1, 3, 3) = (3, 3, 1) = (3, 1, 3)

[a] [b] [c] = (1, 1, 5) ; (1, 4, 2) ; (1, 3, 3) ; (2, 2, 3)

Now, n (S) = 4

Let A be the event of sides forming triangle,

Note:

For triangle

Bigger side < Sum of other two sides

» n (A) = 2

Probability of A = n (A)/n (S) = 2/4 = 0.5

Therefore, probability of forming the triangle is 0.5