Question

7cm long stick cut in three pieces. Length of each piece is natural number.

What is the probability of forming triangle from the three pieces of stick?​

Answer 1

answer: 1 cm

that is the answer

Answer 2

Solution :-

→ Total number of length of pieces can be :-

• 5, 1 , 1
• 1, 5, 1
• 1, 1 , 5
• 4, 2, 1
• 2, 1, 4
• 4, 1, 2
• 2, 4, 1
• 1, 4, 2
• 1, 2, 4
• 3, 2, 2
• 2, 2, 3
• 2, 3, 2
• 1, 3, 3
• 3 , 3 , 1
• 3, 1, 3
• Total = 15 .

now, we know that,

• In ∆ sum of length of any two sides is greater than the third side.

then,

→ Number of sticks that, form a ∆ are :-

• 5, 1 , 1 => 1 + 1 < 5 => Not Possible.
• 1, 5, 1 => 1 + 1 < 5 => Not Possible.
• 1, 1 , 5 => 1 + 1 < 5 => Not Possible.
• 4, 2, 1 => 2 + 1 < 4 => Not Possible.
• 2, 1, 4 => 2 + 1 < 4 => Not Possible.
• 4, 1, 2 => 2 + 1 < 4 => Not Possible.
• 2, 4, 1 => 2 + 1 < 4 => Not Possible.
• 1, 4, 2 => 2 + 1 < 4 => Not Possible.
• 1, 2, 4 => 2 + 1 < 4 => Not Possible.
• 3, 2, 2 => 2 + 2 > 3 => 3 + 2 > 2 => ∆ is Possible.
• 2, 2, 3 => 2 + 2 > 3 => 3 + 2 > 2 => ∆ is Possible.
• 2, 3, 2 => 2 + 2 > 3 => 3 + 2 > 2 => ∆ is Possible.
• 1, 3, 3 => 1 + 3 > 3 => 3 + 3 > 1 => ∆ is Possible.
• 3 , 3 , 1 => 1 + 3 > 3 => 3 + 3 > 1 => ∆ is Possible.
• 3, 1 , 3 => 1 + 3 > 3 => 3 + 3 > 1 => ∆ is Possible.
• Total 6 ∆'s are Possible.

therefore,

→ Required Probability = Favourable outcomes / Total number of outcomes = 6 / 15 = ( 2 / 5 ) (Ans.)

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