2017 AMC 12B Problems/Problem 20
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Problem 20
Real numbers and
are chosen independently and uniformly at random from the interval
. What is the probability that
, where
denotes the greatest integer less than or equal to the real number
?
Solution
when
. The chance that
is
.
when
. The chance that
is
.
This creates an infinite series, where the common ratio is
. The solution is thus