Constructing a Tree Diagram

Oct 13, 2025 by wbrum.org 119 views

Introduction

In this problem, we are presented with a scenario where Shavonda kicks a soccer ball 3 times and makes half the goals she shoots. We need to determine the number of shots she will make. To solve this problem, we will construct a tree diagram to represent the possible outcomes and then calculate the probability of each outcome.

Constructing a Tree Diagram

A tree diagram is a visual representation of the possible outcomes of a situation. It is a useful tool for organizing and analyzing complex problems. In this case, we will use a tree diagram to represent the possible outcomes of Shavonda's soccer shots.

  +---------------+
  |  Shot 1      |
  +---------------+
           /       \
  +---------------+   +---------------+
  |  Goal  |     |  Miss  |
  +---------------+   +---------------+
           |       |
           |       |
  +---------------+   +---------------+
  |  Shot 2      |     |  Shot 2      |
  +---------------+   +---------------+
           /       \       /       \
  +---------------+   +---------------+   +---------------+
  |  Goal  |     |  Miss  |     |  Goal  |     |  Miss  |
  +---------------+   +---------------+   +---------------+
           |       |       |       |       |
           |       |       |       |       |
  +---------------+   +---------------+   +---------------+
  |  Shot 3      |     |  Shot 3      |     |  Shot 3      |
  +---------------+   +---------------+   +---------------+
           /       \       /       \       /       \
  +---------------+   +---------------+   +---------------+   +---------------+
  |  Goal  |     |  Miss  |     |  Goal  |     |  Miss  |
  +---------------+   +---------------+   +---------------+   +---------------+

Possible Outcomes

From the tree diagram, we can see that there are several possible outcomes:

Shavonda makes 3 goals
Shavonda makes 2 goals and 1 miss
Shavonda makes 1 goal and 2 misses
Shavonda makes 0 goals and 3 misses

Calculating the Probability of Each Outcome

To calculate the probability of each outcome, we need to consider the probability of each shot resulting in a goal or a miss. Since Shavonda makes half the goals she shoots, the probability of each shot resulting in a goal is 0.5, and the probability of each shot resulting in a miss is also 0.5.

**Outcome 1: Shavonda makes 3 goals**

Probability of Shot 1 resulting in a goal: 0.5
Probability of Shot 2 resulting in a goal: 0.5
Probability of Shot 3 resulting in a goal: 0.5
Total probability: 0.5 * 0.5 * 0.5 = 0.125

Outcome 2: Shavonda makes 2 goals and 1 miss

Probability of Shot 1 resulting in a goal: 0.5
Probability of Shot 2 resulting in a goal: 0.5
Probability of Shot 3 resulting in a miss: 0.5
Total probability: 0.5 * 0.5 * 0.5 = 0.125

Outcome 3: Shavonda makes 1 goal and 2 misses

Probability of Shot 1 resulting in a goal: 0.5
Probability of Shot 2 resulting in a miss: 0.5
Probability of Shot 3 resulting in a miss: 0.5
Total probability: 0.5 * 0.5 * 0.5 = 0.125

Outcome 4: Shavonda makes 0 goals and 3 misses

Probability of Shot 1 resulting in a miss: 0.5
Probability of Shot 2 resulting in a miss: 0.5
Probability of Shot 3 resulting in a miss: 0.5
Total probability: 0.5 * 0.5 * 0.5 = 0.125

Conclusion

In conclusion, the possible outcomes of Shavonda's soccer shots are:

Shavonda makes 3 goals
Shavonda makes 2 goals and 1 miss
Shavonda makes 1 goal and 2 misses
Shavonda makes 0 goals and 3 misses

The probability of each outcome is 0.125. This means that each outcome is equally likely to occur.

Final Answer

Introduction

In our previous article, we explored the possible outcomes of Shavonda's soccer shots and calculated the probability of each outcome. In this article, we will answer some frequently asked questions about Shavonda's soccer shots.

Q: What is the probability of Shavonda making 3 goals?

A: The probability of Shavonda making 3 goals is 0.125. This means that there is a 12.5% chance that Shavonda will make 3 goals.

Q: What is the probability of Shavonda making 2 goals and 1 miss?

A: The probability of Shavonda making 2 goals and 1 miss is 0.125. This means that there is a 12.5% chance that Shavonda will make 2 goals and 1 miss.

Q: What is the probability of Shavonda making 1 goal and 2 misses?

A: The probability of Shavonda making 1 goal and 2 misses is 0.125. This means that there is a 12.5% chance that Shavonda will make 1 goal and 2 misses.

Q: What is the probability of Shavonda making 0 goals and 3 misses?

A: The probability of Shavonda making 0 goals and 3 misses is 0.125. This means that there is a 12.5% chance that Shavonda will make 0 goals and 3 misses.

Q: Why is the probability of each outcome the same?

A: The probability of each outcome is the same because each shot is an independent event. The outcome of one shot does not affect the outcome of another shot. Therefore, the probability of each outcome is calculated based on the probability of each shot resulting in a goal or a miss.

Q: Can we use this information to make predictions about Shavonda's future soccer games?

A: While this information can provide some insight into Shavonda's soccer skills, it is not a reliable way to make predictions about her future games. There are many factors that can affect the outcome of a soccer game, including the opposing team's skills, the game conditions, and Shavonda's own performance on the day of the game.

Q: How can we use this information in real-life situations?

A: This information can be useful in real-life situations where we need to make decisions based on probabilities. For example, if we are planning a soccer tournament and we need to decide how many goals to expect from each team, we can use this information to make an informed decision.

Conclusion

In conclusion, Shavonda's soccer shots provide a useful example of how to calculate probabilities and make predictions about independent events. While this information can be useful in real-life situations, it is not a reliable way to make predictions about future games.

Final Answer

The final answer is that the probability of each outcome is 0.125, and this information can be used to make informed decisions in real-life situations.