Four real numbers are selected from the interval [0,1] find the probability that at least one of them is greatet than 1/4
Answers
Answer:
This is a problem which might seem difficult at first sight, but is not that bad.
We know the two numbers are drawn randomly. Lets call the first one x and the second y . Furthermore we learn that both are drawn from the uniform distribution on [0,1] . (Actually the distribution is not given, but I chose a simple one to not complicate matters). Because the two events are supposed to be independent (which I also assume), we can draw all possibly combinations as a pair of numbers (x,y) on the square [0,1]×[0,1] .
We need to establish the probability that y≥nx or x≥ny , given a fixed value for n . These two inequalities define two regions in our square. Compute the area of this region. That is your answer. Better yet, compute one area and multiply with 2 . It is just a triangle, no fancy stuff here
Step-by-step explanation: