+274 Two numbers between 0 and 1 on a number line are to be chosen at random. What is the probability that the second number chosen will exceed the first number chosen by a distance greater than 1/4 unit on the number line? Express your answer as a common fraction.
The answer here is incorrect: https://web2.0calc.com/questions/two-numbers-between-0-and-1-on-a-number-line-are-to-be-chosen-at-random-what-is-the-probability-that-the-second-number-chosen-will-exce.
We can divide the number line into 4 equal segments, each of length 1/4. If the second number chosen is in the same segment as the first number, then it will not exceed the first number by a distance greater than 1/4 unit. If the second number chosen is in one of the adjacent segments, then it will exceed the first number by a distance greater than 1/4 unit. Therefore, the probability that the second number chosen will exceed the first number by a distance greater than 1/4 unit is 3/4.
