8E - The law of total probability
8E - Content video: The law of total probability
This video covers the theory and an example of the total law of probability.
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The total law of probability allows us to determine the probability of an event, \(A\), occurring when there are several distinct events which result in, \(A\).
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■ When solving a problem that involves the total law of probability, it is generally useful to represent the sample space using a tree diagram. |
8E - Example 1: Applying the total law of probability
Throughout Roger Federer's professional tennis career, he has served 62% of first serves in. If Federer gets his first serve in he wins 77% of the time. On his second serve he wins 57% of the points. What is the total probability that Federer will win any given point on his serve.
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8E - Example 1: Video solution
8E - Example 1: Practice
Question 1:
Three current Men's singles players, Novak Djokovic, Rafael Nada and Roger Federer, have more than 50 Grand Slam tennis titles between them. With the exception of Andy Murray, these three players have held the position of World Number 1 since 2004. Bruce McAvaney wants to know the total probability of each of these players winning a point during their own service game. Using the law of total probability and the information in the table below, rank the three players from highest to lowest probability of winning a point on their serve. 8E - Example 1: Solutions
Question 1:
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8E - Example 2: Applying the total law of probability
Serena Williams is rewriting the history of Women's Singles in Tennis. In the 2015 Wimbledon Final the probability that Serena won any point on her serve was 0.5822. When Serena's first serve went in, she won 78% of the points. On her second serve, Serena was winning only 35% of points. What was the percentage of first serve that Serena served in for the match?
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8E - Example 2: Video solution
8E - Example 2: Practice
Question 1: ABC Question 2: ABC 8E - Example 2: Solutions
Question 1: ABC Question 2: ABC |