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

Answer: 8/9

Step-by-step explanation:

Taking the probability as

AA = 4/9 AB = 2/9 BA = 2/9 BB = 1/9

These spaces AA, AB, BA, BB is indicates who wins each game.

There is a 2/3 probability that A will win any particular game.

But considering that these events are independent events, the probability that A wins both games is 2/3 and 2/3 which equals to 4/9.

Therefore the probability that A wins at least one match would be 1 - P (BB).

And this gives 1 - (1/9) =

8/9