A and B plays chess everyday . The probability that A beats B in any game is twice the probability that B beats A . The probability that B beats A is three times the probability that the game ends in a draw . What is the probability that the game ends in a draw ?
My working :
P(A wins ) = 2(1- P(A wins ))
P(A wins ) = 2/3
P(B wins) = 3(1-P(A wins)-P(B wins))
P(B wins) = 3(1-2/3-P(B wins ))
P(B wins )=1/4
P(draw)=1-2/3-1/4=1/12 --- my answer
My answer is wrong . I wonder where my mistake is .....
THanks Isomorphism ,
My second attempt :
P(A wins ) = 2[1-P(B wins)-P(draw)]
P(A wins) = 2-2P(B wins)-2P(draw) ------ 1st equation
P(B wins)= 3P(draw) ----- 2nd equation
P(draw) = 1-P(A wins)-P(B wins ) ---- 3rd equation
But after simplifying , i got P(draw)=1/4
My answer is wrong according to the book . Did i get the equations right in the first place ? Thanks for any help ..
Let be the probability of a draw, probability of B winning and the probability of A winning.
Then:
and of course:
or:
so:
as Mr Fantastic has.
Now the ony way out I can see is if the question asked for the odds of a draw since the odds are the ratio of favourable to unfavourable outcomes the odds are .
.