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SMO 2011 Junior Round 1 Question 3

SMO · SMO 2011 Junior Round 1

Question 3

A fair dice is thrown three times. The results of the first, second and third throw are recorded as $x,y,z$, respectively. Suppose $x+y=z$. What is the probability that at least one of $x,y,z$ is $2$?
  1. $\frac1{12}$
  2. $\frac38$
  3. $\frac8{15}$
  4. $\frac13$
  5. $\frac7{13}$