- #1

- 662

- 1

I was reviewing some intro material, and I ended up confused with the issue of

independence with the following problem:

We are given two teams, A,B, playing against each other. A wins with probability

P(A)=0.6 , B wins with P(B)=0.4 (games are played until someone wins.). We also

assume that the outcome of any game is independent from that of any other

game.

**Now** . Here is where I am confused:

Let a string with A in i-th place and B in j-th place denote that A won the i-th

game and B won the j-th game.

I am trying to show that the probability of team A winning two consecutive games

is (0.6)^2 , arguing that the outcome : AA has probability (0.6)(0.6) , since the

outcome of game 2 is (assumed) independent from that of game 1.

**BUT** I am having trouble expressing the event 'AA' as an intersection of two

events E,E' , which I need to do in order to use the rule: P(E/\E')=P(E)*P(E') , (with

/\:= intersection , and * is product)

My sample space is :

{ A,B , AA, AB, BA, BB, AAA, ...}

And I don't see how to express 'AA' as an intersection of events in order to justify

saying that the probability of 'AA' is (0.6)(0.6) . Any Ideas.?.

Thanks.