Answer:
0.2103
Step-by-step explanation:
Since the Distribution is uniform (as it is along a straight line), so we can consider the probabilities as direct areas.
It can represented by a square having an area of
.
Area of whole stick = Length x Breadth = 36 x 36 =1296
This area is equal to probability of 1.
Now when two points are randomly selected, they can be represented as :
and
After breaking from two points, there will be three pieces of stick
1 piece Least length = 6.5 cm
3 piece length = 6.5 x 3 = 19.5 cm
Area of pieces with at least 6.5cm length =
=
=
= ![272.25 cm^{2}](https://tex.z-dn.net/?f=272.25%20cm%5E%7B2%7D)
Probability of resulting pieces having at least 6.5 length = P (6.5 length) = ![\frac{(Area -of -pieces -with-6.5 -length)}{Area-of-stick}](https://tex.z-dn.net/?f=%5Cfrac%7B%28Area%20-of%20-pieces%20-with-6.5%20-length%29%7D%7BArea-of-stick%7D)
P (6.5 length) =
= 0.2103
which is the probability that all of the resulting pieces have length at least 6.5 cm.