Break a stick in 2 places.What's the probability you can make a triangle with the 3 parts?must be end to end.

Answer 1

The answer is 0.25. Not all triplets of three positve numbers can form the sidea of a triangle. Consider, for example 1,2,4. I could come up with a proof if you like.

Answer 2

the three products can sort a triangle if the dimensions of the bigger piece isn't longer than the mixed lengths of both smaller products. in spite of the indisputable fact that, as your question notes, the way you get the three products impacts the answer. let's do #2 first considering #a million relies upon on it. 2) a guy breaks a stick into 2 products at random, grabs the bigger piece, and breaks it into 2 products at random. what's the prospect that he can sort a triangle with the three products? let x = length of the bigger of both products a million/2 ? x ? a million y = higher of both products x is broken into even as x is broken, y ought to no longer be better than a million/2. p(y ? a million/2) = a million - 2(x - a million/2)/x = a million - (2x - a million)/x = a million - 2 + a million/x = a million/x - a million combine over the period [a million/2, a million]. p(y ? a million/2) = ?(a million/x - a million)dx = lnx - x | [Evaluated from a million/2 to at least a million] = [ln1 - a million] - [ln(a million/2) - a million/2] = 0 - a million - ln(a million/2) + a million/2 = ln2 - a million/2 ? 0.1931471 ___________________________ a million) a guy breaks a stick into 2 products at random, grabs somewhat at random, and breaks it into 2 products at random. what's the prospect that he can sort a triangle with the three products? it truly is purely a million/2 the prospect of #2. there's a 50% probability he will grab the shorter stick. if so the conditional probability is 0. there's a 50% probability he will grab the lnger stick. if so the conditional probability is an similar as in question #a million. p(sort a triangle) = (a million/2)(ln2 - a million/2) ? 0.0965735

Answer 3

well if any one particular part of the stick is more then half as long as the total sticks length, then you couldn't make a triangle. So it isn't 100% of the time.
The fist time you break the stick you couldn't break it exactly in half. This is a minute possibility and I imagine it would effect the probability very slightly.
The second time you break the stick you break it from the larger area. This reduces the probability 50%.
On the second break if you break it from the larger part then you must still break this part so neither of these two parts are larger then 50% of the whole stick. This would reduce the probability more but I don't see how you would quantify it to an exact number, but I imagine if you spent some time on this particular area it could be an equation.

Answer 4

You will not be able to create a triangle if any of the pieces is 1/2 or more of the length of the original stick.

The probabilities of this are hard to calculate and depend on how you make the break. For instance, do you make one break and then take one of the two resultant bit and make the second. Or do you mark two breaks to make on the whole initial stick.

But lets assume that you make one break and then move on to make the second. There is then a 1 in 2 chance that your first break will create a stick longer than 1/2 the original. And in the other half of cases there is also a chance that the second break will create a stick longer than 1/2 the original.

So there is less than a 1 in 2 chance of being able to make a triangle.

Answer 5

It really depends on where you broke the stick - for instance, if the stick is 12 inches long, and you break off two one-inch sections, you can't make a triangle. The length of the two shortest pieces added together must always be longer than the third for this to work.

Answer 6

If you consider a straight line a type of triangle (it is in mathematics, since the limit of the angle goes to 0) then the probablility you are able to make a triangle with all line end-to-end. is: first break=50% * second break=50% for a total of 25% chance. For all those saying 100%, THINK before you answer.

Answer 7

It is not 100%. Any side in a triangle must have every 2 side's length added together be longer than the length of the remaining side. Also, any two side's length subtracted from each other must be shorter than the remaining sides length.

Answer 8

SO FOR PROBABILITY
U HAVE 3 PARTS OF STICK AND 2 PART MEET WITH EACH OTHER EVERY TIME

3*2*1/2
6/2
3 OUT OF 3 TIMES U CAN MAKE ITS ONCE OR ONCE AFTER 3 TIMES

Answer 9

not everytime but impossible to calculate
one proof that impossible everytime is:
a meter stick cut in the 2cm and 4cm 2+4<30 so a triangle cant be formed.
there are millions of combinations of numbers in any given length of stick

Answer 10

A triangle's three side's length is a,b,c. The triangle's side's length must be a+b>c and a-b

Answer 11

1:1 Evens 100%