Question

How would I solve the question below:

Answer 1

For a line 10 in long, what is the probability that of 4 randomly distributed points, there will be no distance between two points less than 1 inch?

Answer 2

Hmmm, interesting question. I have some theories on how to solve...

Answer 3

Maybe first try to find out how you would do it with just two points.

Answer 4

Then add in a third point and see how that would affect it.

Answer 5

I have no clue how to solve it with just 2 points

Answer 6

Okay, so think about the points and their distance from the left endpoint:

Answer 7

then we want |x_1-x_2|>1... but how do we get from that to a probability?

Answer 8

We have two random variables.

Answer 9

\[
\Pr(Y\geq X-1, Y\leq X+1)
\]

Answer 10

Hmmm, hold on for a second...
I'm still actually trying to think about how to do this.

Answer 11

How about we do it like this...



\[
x_1+x_2+x_3+x_4+x_5 = 10
\]