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SMO 2009 Senior Round 1 Question 3

SMO · SMO 2009 Senior Round 1

Question 3

If two real numbers $a,b$ are randomly chosen from the interval $(0,1)$, find the probability that the equation $x^2-\sqrt a\,x+b=0$ has real roots.
  1. $\frac18$
  2. $\frac5{16}$
  3. $\frac3{16}$
  4. $\frac14$
  5. $\frac13$