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# Independent Events and Sample Spaces

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Practice Independent Events and Sample Spaces
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# Independent Events and Sample Spaces - Answer Key

## Real World Applications of Independent Events and Sample Spaces

### Vocabulary

• Independent Events
• Dependent Events

### Student Exploration

#### Which University produces the most NBA athletes? What is the likelihood that a top NBA player went to Syracuse University?

In the 2010-2011 season 29 Universities produced four or more NBA players. What is your favorite athletic University? What is the likelihood that an NBA player went to that University? Use the website below to track the Universities that provided multiple NBA players in 2010-2011 (more than four players). Then use the NBA’s stat website to find information about individual players, teams, and divisions of the NBA.
What are the chances that an NBA player went to your favorite athletic University and fulfills a specific play category (i.e. assists, free-throw shots, steals, etc.)?

### Extension Investigation

It is fairly easy to calculate the likelihood that a player in the NBA went to one university, however when we look at a secondary factor that is when Conditional Probability comes into play. Use the two websites above to calculate the following probabilities for NBA players in the 2010-2011 season.

1. What is the probability that a randomly selectedNBA player went to Syracuse University? $\frac{6}{478} = 0.0126 = 1.26%$
2. What is the probability that a randomly selectedNBA player made 35% or more of their 3-point shots (3P%)? $\frac{26}{478} = 0.0544 = 5.44%$
3. What is the probability that a randomly selectedNBA player went to Syracuse University and makes 35% or more of their 3-point shots (3P%)? $\frac{6}{478} \cdot \frac{26}{478}=0.0007=0.07%$
4. What is the probability that a randomly selectedNBA player went to University of Connecticut and stole more than .5 times per game (STPG)? Probability that a player went to U. of Conn. = $\frac{10}{478} = 0.0209 = 2.09%$ Probability that a player steals more than 0.5 per game = $\frac{275}{478} = 0.5753 = 57.53%$ Probability that a random player went to U. of Conn. and stole more than 0.5 per game = $\frac{10}{478} \cdot \frac{275}{478}=0.012=1.2%$
5. What is the probability that a randomly selectedNBA player made less than one personal foul per game (PFPG) and went to UCLA? Probability that a player made less than one personal foul per game (PFPG) more than 0.5 per game = $\frac{74}{478} = 0.1548 = 15.48%$ Probability that a player went to UCLA = $\frac{14}{478} = 0.0292 = 2.92%$ Probability that a random player made less than one personal foul per game (PFPG) more than 0.5 per game and went to UCLA = $\frac{74}{478} \cdot \frac{14}{478}=0.0045=0.45%$

### Connections to other CK-12 Subject Areas

• Theoretical and Experimental Probability