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A and B throw a pair of dice alternately. A wins the game if he gets a total of \[6\] and B wins if she gets a total of \[7\]. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.
A and B throw a pair of dice alternately. A wins the game if he gets a total of \[6\] and B wins if she gets a total of \[7\]. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.
CBSE | Class 12 | Exercise 1 | Maths | NCERT Exemplar | Probability
A and B throw a pair of dice alternately. A wins the game if he gets a total of \[6\] and B wins if she gets a total of \[7\]. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.

Solution:

Let’s take A1 to be the event of getting a total of \[6\]

\[{{A}_{1}}~=\text{ }\left\{ \left( 2,\text{ }4 \right),\text{ }\left( 4,\text{ }2 \right),\text{ }\left( 1,\text{ }5 \right),\text{ }\left( 5,\text{ }1 \right),\text{ }\left( 3,\text{ }3 \right) \right\}\]

And, B1 \[{{B}_{1}}\]  be the event of getting a total of \[7\]

\[{{B}_{1}}~=\text{ }\left\{ \left( 2,\text{ }5 \right),\text{ }\left( 5,\text{ }2 \right),\text{ }\left( 1,\text{ }6 \right),\text{ }\left( 6,\text{ }1 \right),\text{ }\left( 3,\text{ }4 \right),\text{ }\left( 4,\text{ }3 \right) \right\}\]

Let \[P({{A}_{1}})\] is the probability if A wins in a throw = \[5/36\]

And \[P({{B}_{1}})\]is the probability, if B wins in a throw = \[1/6\]

Therefore, the required probability of wining A in his third throw

i

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