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You watch a match between two tennis players: Bill and Tom. You know that one of them is ranked first in the district and the other is ranked 3rd but you don’t know which is which. You also know that the probability that the 3rd ranked player wins any game is p < 1/2, independently of the outcome of other games. You watch ten games. Bill wins eight and Tom wins two. What is the probability that Bill is the first ranked player? Show your work.

Respuesta :

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To solve this problem we need the concepts about Bernoulli variables.

Then we define the two probabilities and states that we have

We have two individuals, Bill and Tom.

Let's consider:

[tex]X = 1[/tex]for the 8/10 probability that Bill is first ranker.

[tex]X = 0[/tex] For the probability that Tom is the first ranker (Or bill is third ranker)

Then,

[tex]P(x=1) = \frac{8}{10}[/tex]

Of 10 games played, Bill has won 8.

P(X=1) = 0.8