Question

In a hockey match, both teams A and B scored same number of goals upto the end of the game,so to decide the winner,the referee asked both the captains to throw a die alternately and decided that the team, whose captains gets a six first will be declared the winner.If the captain of team A was asked to start,find the respective probabilities of winning the match and state whether the decision of the referee was fair or not????? please help me

Answer 1

The probability for CAPTAIN A is 1/6 It will be zero for Captain B if A get 6 or else it will be 1/6 for captain B It is not fair because the winner should be decided based on the talent

Answer 2

Hey !!

Let E₁ , E₂ be two events such that

           E₁ = The captain of team 'A' gets a six

           E₂ = The captain of team 'B' gets a six

Here,                      P (E₁) = $\frac{1}{6}$  , P (E₂) = $\frac{1}{6}$

        P(E₁)' =1 - $\frac{1}{6} = \frac{5}{6}$

        P(E₂)' = $1 - \frac{1}{6} = \frac{5}{6}$

Now, P ( winning the match by team A ) = 1/6 + 5/6 × 5/6 × 1/6 + 5/6 × 5/6 × 5/6 × 5/6 × 1/6 + ..........

        = 1/6 = (5/6)² . 1/6 + (5/4)⁴ . 1/6 + .............

        = 1/6 / $1 - (\frac{5}{6} )$²

        = 1/6 × 36/11

        = 6/11

P ( winning the match by team B ) = $1 - \frac{6}{11} = \frac{5}{11}$

[ NOTE :- If a be the first team and r the common ratio then sum of infinite terms S∞ = $\frac{a}{1-r}$ ]

GOOD LUCK !!