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A game of tennis begins with a serve. Two friends, Mine and Kate will play a series of tennis games until one of them wins two games in a row. Mine serves the the first game with a serve. The serve alternates game by game between Mine and Kate. Mine has a 75% chance of winning a game if she serves and only a 10% chance of winning a game if Kate serves. If all games are independent, what is the probability that Mine is the first one to win two games in a row

Answer :

Applying probability of independent events, it is found that there is a 0.15 = 15% probability that Mine is the first one to win two games in a row.

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If two events, A and B, are independent, the probability of both happening is the multiplication of the probability of each happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

There are two outcomes in which Mine wins two games in a row:

  • Wins the first serving(0.75 probability), then win the second with Kate serving(0.10 probability).
  • Wins the first with Kate serving(0.1 probability), then the second with her serving(0.75 probability).

Thus:

[tex]p = 2 \times 0.1 \times 0.75 = 0.15[/tex]

0.15 = 15% probability that Mine is the first one to win two games in a row.

A similar problem is given at https://brainly.com/question/23855473

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