A stick has a length of 5 units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are shorter than 2 units?
+67 your question has been answered, I have attached a like below.
https://web2.0calc.com/questions/i-m-confused-about-this
+526 The stick is 5 units long. Let the 3 pieces be x, y and 5 - (x + y)
Now this means that
\( 0 ≤ x ≤ 5\)
\( x ≤ y \) and
\(0 ≤ y ≤ 5\)
This graph represents the sample space
Area of sample space \(={1\over 2}× 5×5 = 12.5\) sq. units
Now the probability that all 3 resulting pieces are shorter than 2 units
\( x < 2\)
\(y<2\) and
\(5-(x+y)<2\)
Area of triangle \(={1\over 2}×\sqrt2×\sqrt5\) \(={\sqrt{10}\over 2}\) \(=1.6\) sq. units
∴ P(all 3 pieces are shorter than 2 units) \(={1.6\over 12.5} = 0.128\)
