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

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

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.

   _____________________________

   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

   Reply