**Toolbox:**

- A wins if he gets a total of 6 in a through of pair of dice
- Total of 6 can be obtained
- {\((1\;5)(5\;1)(2\;4)(4\;2)(3\;3)\)}
- Total number of wins for throw of pair of dice=36
- B wins if he gets a total of 7
- Total of 7 can be obtainedby
- {\((1\;6)(6\;1)(2\;5)(5\;2)(3\;4)(4\;3)\)}
- P(A winning)=1-P(A non winning or losing)
- P(B winning)=1-P(B non winning or losing)

A( wins in third throw)

=P(A loses in 1\(^{st}\)and B loses in 2\(^{ed}\) and A wins in 3\(^{rd}\))

=P(A winning)=\(\large\frac{5}{36}\)

=P(A loosing)=1-\(\large\frac{5}{36}\;=\;\frac{31}{36}\)

=P(B wins)\(\large\frac{6}{36}\)

=P(B loosing) =1-\( \large\frac{6}{36}\)=\(\large\frac{30}{36}\)

P(A wins in 3\(^rd\) throw)

=\(\large\frac{31}{36}\;\times\;\frac{30}{36}\;\times\;\frac{5}{36}\)

=\(\large\frac{775}{7776}\)