1978 AHSME Problems/Problem 19
Problem
A positive integer not exceeding
is chosen in such a way that if
, then the probability of choosing
is
, and if
, then the probability of choosing
is
. The probability that a perfect square is chosen is
Solution
Let's say that we will have slips for every number not exceeding
but bigger than
This is to account for the
probability part. Let's now say that we will only have one slip for each number below or equal to
The probability(or
) will then be
Now let's have all the squares under
which are
The probability for these are
The numbers above
that are squares are
We then need to multiply the probability by
so the probability of these are
The answer is
~volkie thangy