Let's suppose we are calculating tennis, where two sets are played.
- The probability of player "A" winning the first set is 50%
- The probability of player "A" winning the second set is 50% (regardless of winning the first set or not, so no dependence)
What is the probability of
- Player "A" winning at least 1 of the 2 sets.
- Player "A" Winning both of the sets.
I am not sure in my method of calculating this, so please explain it.
Thank you very much for your time!
There are four possible mutually exclusive outcomes, where W represents player A winning a set and L his losing it, being WW; WL; LW; LL.
The win or loss of the second set is independent of the first and so p(WL) = p(W)p(L), etc.
Since p(L) = p(W) = 0.5 then the probabilities of each of the four outcomes are all the same and = 0.25 (i.e. 0.5 * 0.5)
Then the probability of A winning at least one set is p(WL) + p(LW) + p(WW) =0.75.
And the probability for A to win both is p(WW) = 0.25