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Home  >>  CBSE XII  >>  Math  >>  Probability
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A and B throw 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.

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  • 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)
=\(\large\frac{31}{36}\;\times\;\frac{30}{36}\;\times\;\frac{5}{36}\)
=\(\large\frac{775}{7776}\)

 

answered Mar 1, 2013 by poojasapani_1
edited Jun 4, 2013 by poojasapani_1
 

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