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Three indistinguishable (fair) dice are thrown simultaneously at random. Find the probability that the sum of the three dice is less than six and that no two dice show the same face (the same number).

I know that the probability that the sum three dice is less than six is 10/216 (or 5/108) and the probability that no two dice show the same face is 5/9. I don't know how to put them all together?!

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    $\begingroup$ It may be helpful to know that $P(A\cap B)=P(A|B)P(B)$. Hint let $A=$ sum of faces is less than six and $B=$ no two dice have same face $\endgroup$
    – Kamster
    Sep 22, 2014 at 3:00
  • $\begingroup$ Yes, I know the formula P(A|B) = P(A∩B)/P(B). But I don't know P(A∩B) $\endgroup$ Sep 22, 2014 at 3:03
  • $\begingroup$ You don't need to know $P(A \cap B)$, that's what you're finding out. You can quite easily calculate $P(A \mid B)$, however. $\endgroup$ Sep 22, 2014 at 3:05
  • $\begingroup$ Exactly, is it quite simple to calculate prob for no same faces. Then given that its easy to calculate prob sum of faces is less than 6 $\endgroup$
    – Kamster
    Sep 22, 2014 at 3:07

1 Answer 1

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The minimal case would be if one dice rolled a 1, another a 2 and a third a 3. The sum of these numbers is not less than six. The probability is zero.

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