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In a hockey match ,both teams …

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In a hockey match ,both teams A and B scored same number of goals upto the end of the match so to decide the winner the referee asked both the captain's to throw a dielectric alternatively and decide that the team ,whose captain gets first six ,will be declared as the winner .If the captain team A starts find the probability of winning match

Posted by Vishaal Velu 7 years ago

CBSE > Class 12 > Mathematics

1 answers

Naveen Sharma 7 years ago

Ans. Let the probability that A gets a six is 1/6.

Hence, p = 1/6 and q = 1- 1/6 = 5/6

Probability of A's Winning =

{tex}P(A) + P(\overline A \space \overline B A) +P(\overline A \space \overline B \space \overline A \space \overline B A) +…………{/tex}

=> p + pq² + pq⁴ +………………

This is in geometric progression, where sum is

{tex}S_n = {p\over 1-q^2}{/tex}

Substituing Value for p and q,

{tex}=> {{1\over 6}\over {1-({5\over 6})^2}} {/tex}

{tex}=> {{1\over 6}\over {1-{25\over 36}}} => {{1\over 6}\over {11\over 36}}{/tex}

Probability of A's winning = 6/11

Probability of B's winning = 1-6/11 = 5/11

ANSWER

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