Ellis Rolls A Number Cube And Spins A Colored Spinner With Three Equal Sections. The Tree Diagram Shows All Possible Outcomes That Can Occur. Pasted-image-1711556451882_7307950d-ec45-47f1-8b51-690abc8534f6 Which Statements Are True? Select Two Answer

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Introduction

In this article, we will delve into the world of probability and explore the concept of a tree diagram. A tree diagram is a visual representation of all possible outcomes of an event, making it easier to understand and analyze the probability of each outcome. We will examine a specific scenario involving a number cube and a colored spinner, and determine which statements are true based on the provided tree diagram.

The Tree Diagram

The tree diagram shows all possible outcomes that can occur when Ellis rolls a number cube and spins a colored spinner with three equal sections. The diagram is a visual representation of the possible combinations of outcomes, making it easier to understand and analyze the probability of each outcome.

Statement 1: The probability of rolling a 1 on the number cube is 1/6.

  • True or False: The probability of rolling a 1 on the number cube is 1/6.
  • Explanation: Since the number cube has 6 equal sections, each section representing a different number, the probability of rolling a 1 is indeed 1/6. This is because there is only one favorable outcome (rolling a 1) out of a total of 6 possible outcomes.

Statement 2: The probability of spinning a red section on the spinner is 1/3.

  • True or False: The probability of spinning a red section on the spinner is 1/3.
  • Explanation: Since the spinner has 3 equal sections, each section representing a different color, the probability of spinning a red section is indeed 1/3. This is because there is only one favorable outcome (spinning a red section) out of a total of 3 possible outcomes.

Statement 3: The probability of rolling a 1 on the number cube and spinning a red section on the spinner is 1/18.

  • True or False: The probability of rolling a 1 on the number cube and spinning a red section on the spinner is 1/18.
  • Explanation: Since the number cube and spinner are independent events, we can multiply the probabilities of each event to find the probability of both events occurring. The probability of rolling a 1 on the number cube is 1/6, and the probability of spinning a red section on the spinner is 1/3. Therefore, the probability of both events occurring is (1/6) × (1/3) = 1/18.

Conclusion

In conclusion, the statements that are true based on the provided tree diagram are:

  • The probability of rolling a 1 on the number cube is 1/6.
  • The probability of spinning a red section on the spinner is 1/3.
  • The probability of rolling a 1 on the number cube and spinning a red section on the spinner is 1/18.

Introduction

In our previous article, we explored the concept of a tree diagram and analyzed the possible outcomes of Ellis rolling a number cube and spinning a colored spinner. In this article, we will answer some frequently asked questions (FAQs) related to the scenario.

Q&A Guide

Q1: What is the probability of rolling a 2 on the number cube?

  • A: The probability of rolling a 2 on the number cube is 1/6. This is because there is only one favorable outcome (rolling a 2) out of a total of 6 possible outcomes.

Q2: What is the probability of spinning a blue section on the spinner?

  • A: The probability of spinning a blue section on the spinner is 1/3. This is because there is only one favorable outcome (spinning a blue section) out of a total of 3 possible outcomes.

Q3: What is the probability of rolling a 3 on the number cube and spinning a red section on the spinner?

  • A: The probability of rolling a 3 on the number cube and spinning a red section on the spinner is (1/6) × (1/3) = 1/18. This is because the number cube and spinner are independent events, and we can multiply the probabilities of each event to find the probability of both events occurring.

Q4: What is the total number of possible outcomes when Ellis rolls a number cube and spins a colored spinner?

  • A: The total number of possible outcomes is 6 (number cube) × 3 (spinner) = 18. This is because there are 6 possible outcomes for the number cube and 3 possible outcomes for the spinner, making a total of 18 possible outcomes.

Q5: What is the probability of rolling a 1 on the number cube and spinning a blue section on the spinner?

  • A: The probability of rolling a 1 on the number cube and spinning a blue section on the spinner is (1/6) × (1/3) = 1/18. This is because the number cube and spinner are independent events, and we can multiply the probabilities of each event to find the probability of both events occurring.

Q6: What is the probability of spinning a red section on the spinner and rolling a 4 on the number cube?

  • A: The probability of spinning a red section on the spinner and rolling a 4 on the number cube is (1/3) × (1/6) = 1/18. This is because the number cube and spinner are independent events, and we can multiply the probabilities of each event to find the probability of both events occurring.

Q7: What is the probability of rolling a 2 on the number cube and spinning a blue section on the spinner?

  • A: The probability of rolling a 2 on the number cube and spinning a blue section on the spinner is (1/6) × (1/3) = 1/18. This is because the number cube and spinner are independent events, and we can multiply the probabilities of each event to find the probability of both events occurring.

Q8: What is the probability of rolling a 5 on the number cube and spinning a red section on the spinner?

  • A: The probability of rolling a 5 on the number cube and spinning a red section on the spinner is (1/6) × (1/3) = 1/18. This is because the number cube and spinner are independent events, and we can multiply the probabilities of each event to find the probability of both events occurring.

Q9: What is the probability of spinning a blue section on the spinner and rolling a 6 on the number cube?

  • A: The probability of spinning a blue section on the spinner and rolling a 6 on the number cube is (1/3) × (1/6) = 1/18. This is because the number cube and spinner are independent events, and we can multiply the probabilities of each event to find the probability of both events occurring.

Q10: What is the probability of rolling a 3 on the number cube and spinning a blue section on the spinner?

  • A: The probability of rolling a 3 on the number cube and spinning a blue section on the spinner is (1/6) × (1/3) = 1/18. This is because the number cube and spinner are independent events, and we can multiply the probabilities of each event to find the probability of both events occurring.

Conclusion

In conclusion, we have answered some frequently asked questions related to the scenario of Ellis rolling a number cube and spinning a colored spinner. By understanding the concept of probability and analyzing the tree diagram, we can determine the probability of each possible outcome and gain a deeper understanding of the scenario.