Geometric probability

Question

Two numbers are chosen at random from the interval (-1,1). If we know their sum is negative, find the probability that the first number is less than 1/2 and its square is less than the second number.

Answer 1

Since the sum is negative, they are both negative.

 

Therefore they are both less than 1/2, with probability 100%

 

Squaring a negative number results in a positive number which

cannot be less than the second number, which is negative.

So the probability that the square is less is zero.

 

So the probability, as written and stated, is zero.