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  • It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they will win alterna

It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they will win alternately is

Option: 1

\frac{5}{72}


Option: 2

\frac{5}{36}


Option: 3

\frac{19}{27}


Option: 4

None of these


Answers (1)

best_answer

The probability of A winning in a game \mathrm{=P(A)=\frac{6}{12}=\frac{1}{2}}

The probability of B winning in a game \mathrm{=P(B)=\frac{4}{12}=\frac{1}{3}}

The required probability \mathrm{=P(A \cap B \cap A)+P(B \cap A \cap B)}

\mathrm{=P(A) \cdot P(B) \cdot P(A)+P(B) \cdot P(A) \cdot P(B)=\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{2}+\frac{1}{3} \cdot \frac{1}{2} \cdot \frac{1}{3}=\frac{5}{36} .}

Posted by

Suraj Bhandari

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