Note: 1) Brace yourself, spoon feeding is about to begin.
2) first two dice --- implies two blue dice.
3rd dice --- implies red dice.
Point 1) What's asked in question?
ans) P(person actually won | person claimed that he won) = ?
Point 2) Why 1/216 isn't the ans.?
ans) After reading this question, first thought that arrives is....ummm...isn't 1/216 the correct ans. (I bet most people must have thought this).
But read point 1 (above), point 3 (below) and now read question 2-3 times.
Makes Sense now?
(1/216 is just the probability that person won! and this isn't what's asked in the question!)
Point 3) Elaborating srestha's ans:
ans)
4 cases arise:
person won and 1 came on red dice ---- person tells the truth i.e. person tells he won.
person won and 2 or 3 or 4 or 5 or 6 came on red dice ---- person tells the lie i.e. person tells he lost.
person lost and 1 came on red dice ---- person tells the truth i.e. person tells he lost.
person lost and 2 or 3 or 4 or 5 or 6 came on red dice ---- person tells the lie i.e. person tells he won.
Therefore, person claims "he won" in 2 cases:
person won and 1 came on red dice
person lost and 2,3,4,5,6 came on red dice
Hence, P(person actually won | person claimed that he won) = ??
P(person actually won and person claimed he won)
= ---------------------------------------------------------------------------------------------------------------
P(person actually won and person claimed that he won) + P(person actually lost and person claimed that he won)
(6 came on first dice and 6 came on 2nd dice and 1 came on 3rd dice)
= -----------------------------------------------------------------------------------------------------------------
(6 came on first dice and 6 came on 2nd dice and 1 came on 3rd dice) + (double 6 didn't come on first 2 dice throws and (2 or 3 or 4 or 5 or 6 came on 3rd dice))
1/216
= ------------------------------
1/216 + (35/36)(5/36)
1
= ------------------------------
1+175
1
= ------------------------------
176
That's it folks!
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and kudos to srestha coming up with the correct ans.
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