satellite plz help with the probability question!!!!

Question

anonymous · Answer

yup

akshay_budhkar · Answer

http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e3a8bc10b8bf47d0660238b#/groups/mathematics/updates/4e3a8bc10b8bf47d0660238b#/groups/mathematics/updates/4e3a8bc10b8bf47d0660238b

akshay_budhkar · Answer

try it hafiz..

anonymous · Answer

hello

akshay_budhkar · Answer

hello.. i tried it.. no use

anonymous · Answer

link isn't working for me

akshay_budhkar · Answer

we can solve here

akshay_budhkar · Answer

a rod is divided in 4 parts.. probability that it is a quadrilateral?

anonymous · Answer

ok it is the same problem as last time yes?

akshay_budhkar · Answer

yes

anonymous · Answer

not sure what you mean.  i meant use the second proof in the paper i sent you. not the volume one, but the line segment one.

anonymous · Answer

start an page 186 at the line "construction of an n-gon will be impossible of AB is longer than 1/2"  do you see where i mean?

anonymous · Answer

of course replace n by 4

anonymous · Answer

i am here.

anonymous · Answer

i may be easier to do this in chat, or quicker, but i can write the idea of the proof here.  i am just mimicking the proof i sent you in the pfd .

akshay_budhkar · Answer

you can come in chat?

anonymous · Answer

you have a "rod" stick whatever and you are going to break it into 4 parts by picking 3 points uniformly at random, and the question is what is the probability that you can make a quadrilateral

akshay_budhkar · Answer

yes

anonymous · Answer

you already know the answer is 1/2 
so far correct.  so we just need the proof

akshay_budhkar · Answer

yes

anonymous · Answer

first trick to to say that the rod has length one so we can dispense with ratios

akshay_budhkar · Answer

ya

anonymous · Answer

so it looks something like this 
0 --------------a-----------------b--------------------------c-------------------------1
where a, b, c are the points chosen at random to break up the rod

anonymous · Answer

now the question is "when would you not get a quadrilateral\"

anonymous · Answer

now i am just reading along what i sent, replacing n by 4

anonymous · Answer

construction of a quadtrilateral will be impossible if 
$$\overline{0a}$$ is bigger than one half, i.e. if all three points are to the right of the midpoint of the segment.  the probability that one is to the right is 1/2 and all three to the right would be 
$$(\frac{1}{2})^3$$

anonymous · Answer

the same is true for the other three  segments, and the probability that each of them  is bigger than one half is also 1/8
so the probability of failure is 4 times 1/8 = 1/2 and therefore so is the probability of success.