A player serving in tennis has two chances to get a serve into play. If the first serve is out, the player serves again. If the second serve is also out, the player loses the point. Observe the probabilities based on four years of the Wimbledon Championship. ?(1st serve in)=0.59P(1st serve in)=0.59 ?(win point | 1st serve in)=0.73P(win point | 1st serve in)=0.73 ?(2nd serve in | 1st serve out)=0.86P(2nd serve in | 1st serve out)=0.86 ?(win point | 1st serve out and 2nd serve in)=0.59P(win point | 1st serve out and 2nd serve in)=0.59 Make a tree diagram for the results of the two serves and the outcome, win or lose, of the point. The branches in your tree have different numbers of stages depending on the outcome of the first serve. What is the probability that the serving player wins the point? Report your answer to four decimal places.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
A player serving in tennis has two chances to get a serve into play. If the first serve is out, the player serves again. If the second serve is also out, the player loses the point. Observe the probabilities based on four years of the Wimbledon Championship.
Make a tree diagram for the results of the two serves and the outcome, win or lose, of the point. The branches in your tree have different numbers of stages depending on the outcome of the first serve.
What is the probability that the serving player wins the point? Report your answer to four decimal places.
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