Prob Player A wins single chess match against Player B is 0.4; prob. wins both games

Two chess players are competing in 2 games against each other. The probability for player A to win a single match is 0.4 and the probability to win the contest is also 0.4.

1) What is the probability for B to win a single match?
2) What is the probability for the contest to end in a draw?

here is what i've tried for 1 :

P(A wins,B wins)+p(B wins,A loses)=(0.4*0.6)+(0.6*0.4)=0.48
but the answer is wrong ,i don't know whats wrong with that logic .

hasanneo said:

Two chess players are competing in 2 games against each other. The probability for player A to win a single match is 0.4 and the probability to win the contest is also 0.4.

1) What is the probability for B to win a single match?
2) What is the probability for the contest to end in a draw?

here is what i've tried for 1 :

P(A wins,B wins)+p(B wins,A loses)=(0.4*0.6)+(0.6*0.4)=0.48
but the answer is wrong ,i don't know whats wrong with that logic .

Click to expand...

Chess games can end in draws. Have you accounted for this at all?

. . .first game:
. . . . .A wins: 0.4
. . . . .they draw: d
. . . . .B wins: b

Branching from this for the second game, the ways A can with the two-game contest are:

. . . . .A wins both games
. . . . .A wins the first game, and the second game is a draw
. . . . .the first game is a draw, and A wins the second

What expressions do you get for these? Summing and setting equal to the given probability, what do you get for the value of "d"? And so forth.

Please be complete. Thank you!

hasanneo said:

Two chess players are competing in 2 games against each other. The probability for player A to win a single match is 0.4 and the probability to win the contest is also 0.4.

1) What is the probability for B to win a single match?
2) What is the probability for the contest to end in a draw?

here is what i've tried for 1 :

P(A wins,B wins)+p(B wins,A loses (wins?))=(0.4*0.6)+(0.6*0.4)=0.48
but the answer is wrong ,i don't know whats wrong with that logic .

Click to expand...

You are incorrectly assuming here that P(B wins a single game) = 1-0.4 = 0.6.
But there are three ways a chess game can end: A wins, B wins or Stalemate (draw).

You are also misinterpreting the question. You are attempting to find the probability that B will win exactly one of the two games. This is not what is being asked.