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

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

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