Q. 275.0( 2 Votes )

In a hockey match

Answer :

As captain of team A has started to throw the die, he may win in the first throw or third or fifth and so on.


Team B can win in 2nd throw or 4th or 6th and so on


As probability of getting 6 on a die = 1/6 = P(6)


P(6’) represents event of not getting 6 = 5/6


Let P(A) represents the probability that team A wins the game and P(B) represents the probability that team B wins the game.


P(A) = P(6) + P(6’)P(6’)P(6) + P(6’)P(6’)P(6’)P(6’)P(6)+…to ∞


P(A) =


P(A) =


Clearly it forms an infinite GP and sum of infinite GP is given by where a is the first term and r is common ratio.


Here a = 1 and r = (5/6)2


P(A) =


Similarly,


P(B) = P(6’)P(6) + P(6’)P(6’)P(6’)P(6) + … to ∞


P(B) =


P(B) =


Clearly it forms an infinite GP and sum of infinite GP is given by where a is the first term and r is common ratio.


Here a = 1 and r = (5/6)2


P(B) =


Clearly, P(A) > P(B)


Hence, there is more chance of winning of team A.


Umpire’s decision is unfair. He has favoured team A.


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