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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

Two fair dice are rolled one time. If the probability to roll the sum that came up on of the top faces is 5/36 then what is the probability for one of the top faces to show a 3?

There are only two sums that have a 5/36 probability of happening: 6 and 8. We can clearly see this by taking a look at the sample space for this experiment:

1 | 2 | 3 | 4 | 5 | 6 | |

1 | 2 | 3 | 4 | 5 | 6 | 7 |

2 | 3 | 4 | 5 | 6 | 7 | 8 |

3 | 4 | 5 | 6 | 7 | 8 | 9 |

4 | 5 | 6 | 7 | 8 | 9 | 10 |

5 | 6 | 7 | 8 | 9 | 10 | 11 |

6 | 7 | 8 | 9 | 10 | 11 | 12 |

The possible sums can be formed by 10 possible pairs of numbers:

Out of these pairs, only 3 contain the number 3. So there is a probability of:

for the number 3 to be on one of the upturned faces.