The odds are 2 to 1 that, when A play B in tennis, A wins. Suppose that A and B play two matches. What is the probability that A wins at least one match?

Question

anonymous · Answer

The simple events are 

E1:{AA}  E2:{AB}  E3:{BA}  E4:{BB}

anonymous · Answer

for example AB means A won the first mach and B wins the second match

anonymous · Answer

My books says that these events are not equally proable, since A wins 2 to 1 eveytime A and B play.  They assign the follwing proablilites:

P(E1):=4/9,    P(E2)=2/9,  P(E3)=2/9  and P(E4):=1/9

anonymous · Answer

My question is:  How did they get this proablilites?

anonymous · Answer

P(A wins at least 1 match) = 1-P(A loses both matches)
                                   =1-1/9 = 8/9

anonymous · Answer

okay, but how did they come up with the probablilityes?