SOLUTION: A and B plays 12 games of chess of which 6 are won by A, 4 are won by B and two ends on a tie. They agree to play a tournament consistian of 3 games. Find the probability that A wi

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Question 1177054: A and B plays 12 games of chess of which 6 are won by A, 4 are won by B and two ends on a tie. They agree to play a tournament consistian of 3 games. Find the probability that A wins all three games.
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
12 games: A wins 6, B wins 4 and 2T
play a tournament consisting of 3 games.

P(A wins 3 games) = (1/2)(1/2)(1/2) = 1/8

Wish You the Best in your Studies.


Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
A and B plays 12 games of chess of which 6 are wonby A, 4 are won by B and two ends on a tie.
They agree to play a tournament CONSISTING of 3 games.
Find the probability that A wins all three games.
~~~~~~~~~~~~~~~


This problem is,  actually,  a standard problem of this class,  but expressed in slightly unusual terms,
which may create difficulties to you in understanding its meaning.

Therefore,  I will re-formulate this problem  EQUIVALENTLY  in familiar terms. 

    +------------------------------------------------------------------------+
    |   In a bag, there are 6 black balls, 4 white balls and 2 blue balls.   |
    |   You draw 3 of these balls randomly without replacement.              |  
    |   What is the probability to draw 3 black balls ?                      |
    +------------------------------------------------------------------------+


SOLUTION 

The probability to win the first of the 3 games is  P(win 1st) =  = .


The probability to win the second of the 3 games is  P(win 2nd) = .


The probability to win the third of the 3 games is  P(win 1st) =  = .


The probability to win all 3 games is  


    P = P(win 1st)*P(win 2nd)*P(win 3rd) =  =  = .    ANSWER

Solved.

-------------

The solution by @ewatrrr is  INCORRECT,  and her interpretation of the problem is  INCORRECT,  too.

So,  ignore her post for your safety.



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