Q. 354.5( 2 Votes )

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

Answer :

Given that teams A and B scored same number of goals.


It is asked captains of A and B to throw a die.


The first who throw 6 awarded a prize.


P(S6) = P(getting 6)



P(SN) = P(not getting 6)




It is given A starts the game, A wins the game only when he gets 6 while throwing die in 1st,3rd,5th,…… times


Here the probability of getting 6 on throwing a die is same for both the players A and B


Since throwing a die is an independent event, their probabilities multiply each other


P(Awins) = P(S6) + P(SN)P(SN)P(S6) + P(SN)P(SN)P(SN)P(SN)P(S6) + ……………




The series in the brackets resembles the Infinite geometric series.


We know that sum of a infinite geometric series with first term ‘a’ and common ratio ‘o’ is .






P(Bwins) = 1-P(Awins)




Since the probabilities if winnings of A and B are not equal, the decision of the referee is not fair


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :