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SMO 2025 Junior Round 1 Question 5

SMO · SMO 2025 Junior Round 1

Question 5

A fair dice with numbers 1, 2, 3, 4, 5 and 6 on its six faces respectively was rolled twice. In the first and second rolls, the dice landed on numbers $a$ and $b$ respectively. What is the probability that the equation $x^2+ax+b=0$ has two distinct real roots?
  1. $\frac5{12}$
  2. $\frac49$
  3. $\frac{17}{36}$
  4. $\frac12$
  5. $\frac{19}{36}$