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Suppose that Dice $1$ has five faces numbered $1$ to $5,$ each of which is equally likely to occur once the dice is rolled. Dice $2$ similarly has eight equally likely faces numbered $1$ to $8.$ Suppose that the two dice are rolled, and the sum is equal to $8.$ Conditioned on this, what is the chance that the Dice $1$ rolled a number less than or equal to $2?$

  1. $1 / 4$
  2. $1 / 3$
  3. $1 / 2$
  4. $2 / 7$
  5. $2 / 5$

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