suppose you got two sticks the length of one is three times that of the smaller stick. break the larger stick randomly into two pieces. then the probability that you can make a triangle using the three pieces is
Answers
Answered by
0
The question is, if x and y are random numbers between 0 and 1 (with the obvious unstated assumption that the distribution of probabilities is uniform), how likely is it that the differences between them and 0 and 1 are such that none is greater than 1/2?
We can ignore the possibility that :
x=y because it has zero probability.
If x is less than y, those differences are x, y − x, and 1 −y ; each must be less than 1/2
Each of these three inequalities tells us that the points in the xy - plane lie to one side of a straight line. Together they determine a triangle of area 1/8 (it’s half of a quarter of a unit square).
For the Broken sticks that form a triangle.
Our assumption that x>y determines a region of area 1/2, and since the case of y>x is symmetrical, we conclude that the proportion of (x,y) pairs suited to making triangles is 1/4
Answer :
1/4
Similar questions