Construct a tree diagram showing all possible results when three fair coins are tossed. Then list the ways of getting the following result. at least two heads Construct a tree diagram showing all possible results when three fair coins are tossed. Choose the correct diagram below. O A. H H T H T T HHH HHT HTH HTT THH THT TTH TTT B. O A. TTT, HTT, THT, TTH, HHT, HTH, THH, HHH OB. HHH O C. TTH, THT, HTT, TTT D. HHT, HTH, THH, HHH H H H T H T T HHH HHT HTH HTT HHH HHT HTH HTT O C. H Select the correct choice below that lists the appropriate branches for the ways of getting at least two heads. T H T V V V V T || | || | | HHH HHH HTH HTT HHT THT TTH TTT

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Educational Content on Tree Diagrams for Coin Tosses**

**Title:** Exploring Probability with Tree Diagrams

**Concept:** Constructing Tree Diagrams for Tossing Coins

---

**Introduction:**

In probability, tree diagrams are useful tools for illustrating all possible outcomes of an event. Here, we will explore how to construct a tree diagram for tossing three fair coins and identify ways to get at least two heads.

---

**Task:**

Construct a tree diagram showing all possible results when three fair coins are tossed. Then, list the ways of obtaining at least two heads.

---

**Tree Diagram Options:**

**Option A:**

- Start with the first coin: Head (H) or Tail (T).
- For each outcome, the second coin also has two possibilities: H or T.
- Continue branching for the third coin.
- Outcomes:
  - HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

**Option B:**

- Another arrangement of outcomes for three coin tosses is displayed.
- Outcomes:
  - HHH, HHT, HTH, HTT, HHH, HHT, HTH, HTT

**Option C:**

- A different sequence is presented.
- Outcomes:
  - HHH, HHH, HTH, HTT, HHT, HTH, TTH, TTT

**Conclusion:**

Select the correct tree diagram and choose the outcomes that ensure at least two heads.

---

**Question:**

Select the correct choice below that lists the appropriate branches for getting at least two heads:

- **A.** TTT, HTT, THT, TTH, HHT, HTH, THH, HHH
- **B.** HHH
- **C.** TTH, THT, HTT, TTT
- **D.** HHT, HTH, THH, HHH

---

**Analysis:**

- The correct choice is **D**: HHT, HTH, THH, HHH. These outcomes represent getting at least two heads from the tosses.

This exercise helps in understanding how tree diagrams organize and visualize possible outcomes in probability scenarios.
Transcribed Image Text:**Educational Content on Tree Diagrams for Coin Tosses** **Title:** Exploring Probability with Tree Diagrams **Concept:** Constructing Tree Diagrams for Tossing Coins --- **Introduction:** In probability, tree diagrams are useful tools for illustrating all possible outcomes of an event. Here, we will explore how to construct a tree diagram for tossing three fair coins and identify ways to get at least two heads. --- **Task:** Construct a tree diagram showing all possible results when three fair coins are tossed. Then, list the ways of obtaining at least two heads. --- **Tree Diagram Options:** **Option A:** - Start with the first coin: Head (H) or Tail (T). - For each outcome, the second coin also has two possibilities: H or T. - Continue branching for the third coin. - Outcomes: - HHH, HHT, HTH, HTT, THH, THT, TTH, TTT **Option B:** - Another arrangement of outcomes for three coin tosses is displayed. - Outcomes: - HHH, HHT, HTH, HTT, HHH, HHT, HTH, HTT **Option C:** - A different sequence is presented. - Outcomes: - HHH, HHH, HTH, HTT, HHT, HTH, TTH, TTT **Conclusion:** Select the correct tree diagram and choose the outcomes that ensure at least two heads. --- **Question:** Select the correct choice below that lists the appropriate branches for getting at least two heads: - **A.** TTT, HTT, THT, TTH, HHT, HTH, THH, HHH - **B.** HHH - **C.** TTH, THT, HTT, TTT - **D.** HHT, HTH, THH, HHH --- **Analysis:** - The correct choice is **D**: HHT, HTH, THH, HHH. These outcomes represent getting at least two heads from the tosses. This exercise helps in understanding how tree diagrams organize and visualize possible outcomes in probability scenarios.
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