hartnn
  • hartnn
If a line segment is cut into 3 parts, what is the probability that those 3 parts can form a triangle ?
Probability
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
hartnn
  • hartnn
50% ??
mayankdevnani
  • mayankdevnani
For example, if I have a length of rope 10. I can cut it into 1-1-8 (no triangle) Or 2-3-5 (no triangle) Or 4-4-2 (triangle) Or 3-3-4 (triangle).
mayankdevnani
  • mayankdevnani
just apply triangle inequality.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

hartnn
  • hartnn
your point is , sum of two sides of triangle must be > 3rd ?
mayankdevnani
  • mayankdevnani
yaaa
hartnn
  • hartnn
used that, solved it, got 50% want to verify whether its correct....
mayankdevnani
  • mayankdevnani
verify- 3,3,3(forms triangle) sum of two sides of triangle must be > 3rd(6>3)
hartnn
  • hartnn
i would like to restate : sum of two sides of triangle must be > or = 3rd
mayankdevnani
  • mayankdevnani
right
mayankdevnani
  • mayankdevnani
6>3(3+3>3) PROVE IT!
mayankdevnani
  • mayankdevnani
thus, it proves it forms a triangle!!! @hartnn can you understand??
hartnn
  • hartnn
yes, that forms equilateral triangle. but i want to find the probability.
mayankdevnani
  • mayankdevnani
i think probability is outcome/parts=10/3
hartnn
  • hartnn
probability can never be >1 -_-
anonymous
  • anonymous
You want that 1 of the segments is not >0.5 of the stick.
anonymous
  • anonymous
I think the probability here may be dependent on the decision procedure that you choose the 3 parts in. Can I assume you throw 2 darts simultaneously at the stick, and these points are the points that you cut it?
hartnn
  • hartnn
even i can't say what can be assumed, this was the question...and i found it mathematically that this probability is 50% , just want to see new approaches and verify my answer. so , go ahead and try it...
anonymous
  • anonymous
Well, using my method it's less than 50% that form a triangle. Call where the first dart lands X|dw:1354373456702:dw|, in the half of the stick called A Disregard the 'A' half of the stick. Now, the chance that the second dart lands in A, leaving there a segment of >0.5 is 50%. However...
anonymous
  • anonymous
It is possible that the second dart lands in B AND the second dart lands in A AND STILL there would be 1 segment >0.5 length of the stick.|dw:1354373603207:dw| So the chance of a non-triangle, because of this, is LESS than 50%. But it absolutely matters which procedure you use to cut.
anonymous
  • anonymous
For example, you could choose the longer of the 2 parts that the first dart cuts in half, and throw the second dart against this part of the stick.
hartnn
  • hartnn
i didn't get u entirely, but got some idea on what u saying.... moreover, i think there's a numerical answer to this, rather than inequality.(like >0.5)....
anonymous
  • anonymous
Yes, there is (not sure how to yet). Do you understand my reasoning that 1 side of the triangle cannot be >0.5 of the original stick (that is, cannot be > than the sum of the other 2 sides)?
hartnn
  • hartnn
ofcourse, i got that when i solved, and that gave me 50%.
anonymous
  • anonymous
By what logic?
hartnn
  • hartnn
ok, i'll show what i had done in test.
anonymous
  • anonymous
I'll type up my try to work out a numerical answer at the same time
hartnn
  • hartnn
|dw:1354374054772:dw|
hartnn
  • hartnn
@UnkleRhaukus can u have a look and share any ideas ?? same for Callisto.
anonymous
  • anonymous
Assume dart 1 has an equal probability of landing anywhere on the stick. By definition, it lands on the half of the stick called A. Equal probability of landing anywhere on there. Now, your question is equivalent to saying: 'what is the probability that the 2nd dart will not leave a part-stick of >0.5 length?' There are 2 ways of making a part-stick of >0.5 length: -dart 2 lands in half A also -this happens|dw:1354374314148:dw|
anonymous
  • anonymous
The second way works as there is a hole of length >=0.5 in the middle. Working it out: Prob(dart 2 lands in B)=0.5 Prob(x <= y)=(y/0.5) where y is a length measured from the right, and 0.5 is a length.
hartnn
  • hartnn
isn't this getting complicated ? for me, yes.... what wrong in my answer ?
anonymous
  • anonymous
Have I misunderstood the question? It looks like for you a is the random variable, and x, y and z are fixed. How are you making your triangle?
hartnn
  • hartnn
yeah, a is fixed. i will make a triangle with sides x,y,z.
UnkleRhaukus
  • UnkleRhaukus
so on of the triangles lengths must be greater than the sum of the other two , you need both darts to cut the string on different sides of the half way point , assuming the first dart land one side, the probability that second dart land on the opposite half of the string is 50%
UnkleRhaukus
  • UnkleRhaukus
one*
hartnn
  • hartnn
so, what @henpen said here 'Prob(dart 2 lands in B)=0.5' its straightaway 50% ?
anonymous
  • anonymous
My problem is that there are ways of the too large side being formed even if they land in the opposite sides, for example:|dw:1354375141124:dw|
anonymous
  • anonymous
|dw:1354375288008:dw| We want \[p+q<0.5\]
anonymous
  • anonymous
By definition, \[p<0.5\] and \[q<0.5\] So it seems in the second case it is 50% (not 50% overall)|dw:1354375464988:dw|
anonymous
  • anonymous
So overall I'd say 75% (as in the first case it's 100% not going to form a triangle (100% of 50%=50% overall) and in the second case it's 50% not going to form a triangle (50% of 50%=25%)).
UnkleRhaukus
  • UnkleRhaukus
hmm,
hartnn
  • hartnn
huh ?
hartnn
  • hartnn
25% sure ?
anonymous
  • anonymous
fairly sure

Looking for something else?

Not the answer you are looking for? Search for more explanations.