**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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