I have a problem with this exercise, which says:
I have to divide a line segment into two parts, where I select a point randomly. I need to find the probability that the larger segment is at least 3 times shorter. Here I have to assume a uniform distribution.
My first idea is to look at a line from zero to one. If I choose x < 1/4 and x>3/4, then how do I find the probability that the larger segment is at least 3 times shorter? I don't know how to do this.
Thanks in advance.
Best Answer
If any value of $x$ is as likely as any other value of $x$ that you choose, then the probability is simply the fraction of the entire line segment that contains the points that satisfy the condition.
You already have the correct parts of the line segment. What fraction of the total line segment is it? There's your answer.