Probability and odds question

Imagine there are two tennis players (X and Y) that are evenly matched. If they play 4 matches, what are the odds that one of them will win all four?

Now assume there are two tennis players that may or may not be evenly matched. They play 4 matches and player X wins all 4 matches. What are the odds that player Y is at least as good if not better than player X?

Re: Probability and odds question

Hey ItsOmar.

You should think about whether the number of matches one player wins is modeled by a Binomial random variable.

If each match is independent and each player has the same probability of winning, then this is a Binomial distribution with n matches and probability p for a fixed player.

If the probabilities change, but are independent, you need to use a probability generating function.

If the probabilities depend on what happened in the outcome of the last match, you need to use a Markov Chain model.

If it is more complex than this, you will probably need to use simulation models on a computer.

Re: Probability and odds question

Thanks for the help!

Assuming each match is independent, I used the binomial distribution and got an answer of .0625 for the first question. I doubled it however since either player could potentially win all four. So.. 12.5%

As for the second question, I'm still completely lost.

Re: Probability and odds question

For the second one you need to do a Hypothesis test.

If you assume a binomial with parameters n = 4, and p = probability of player X winning, then if your hypothesis is for player Y being at least as good or better than X, then it means that p < 0.5.

So now you are testing that H0: p < 0.5, H1: p > 0.5.

Your firstly have to estimate p with your sample (it will be 1 or close to 1 given your sample). Then you need to construct a test statistic (it will be from a binomial distribution), and show that the p-value for H0 is small enough to reject H0.