Probability of Winning and Losing in a 3-Round Game

[campa]

Hi,

Can someone please solve this sum either by drawing a rook diagram or any other way

the question goes like: There are two teams A and B. The probability of A winning is 50% and the probability of B winning is 40%. These two teams take part in 3 same rounds.
1) What is the probability of A winning all three rounds?
2) What is the probability of the game ending without any winnings or losing
3)What is the probability of the game ending without two winnings or losing

 

[honestrosewater]

1) Are these events independent or dependent?
2) Same question.
3) Same question.

 

[kleinwolf]

I think you can write : p(wa)=.5, p(wb)=.4

Then it seems logical to assume either A wins or B wins, but not both (incompatible events)..hence p(wa or wb)=p(wa)+p(wb)=.9=1-p(la and lb)

hence p(la and lb)=.1 so it could be that nobody wins with prob. .1 at each round.

does this help ?

 

[campa]

in the second and third questions it should be a draw I guess and but there are three rounds so doesn't that make any difference when solving this problem?

 

[honestrosewater]

in the second and third questions it should be a draw I guess and but there are three rounds so doesn't that make any difference when solving this problem?

Yes. You need to find the probability of multiple events occurring together. Are the events independent or dependent? If A winning round 1 and A winning round 2 and A winning round 3 are independent events, the probability of A winning all three rounds is the product of the probability of each event occurring: P(W_A) * P(W_A) * P(W_A).

 

[kleinwolf]

I suppose there are no dependences between rounds...I think the traps were just :

a) it comes out that lose_b and lose_a are dependent
b) if A loses and B loses, then neither wins, but nobody lose which seems contradictory

 

[campa]

I guess these are independent events. thanks for the help