Two fair dice are rolled. Let B = the event that the sum is odd, A = the event that the sum is 7 or more, and C= the event that at least one die shows a 2. For these three events, which pairs of events are independent and which pairs are dependent? ..... How can pairs of events be shown to be independent? O A. Events E and F are independent when P(E|F) = P(E) and P(F|E) # P(F). O B. Events E and F are independent when P(E|F) # P(E) and P(F|E)#P(F). OC. Events E and F are independent when P(E|F) = P(E) and P(F|E) = P(F). O D. Events E and F are independent when P(E|F)#P(E) and P(F|E) = P(F). Which pairs of events are independent? Select all that apply. O A. events A and C O B. events B and C O C. events B and A O D. No pairs are independent. Which pairs of events are dependent? Select all that apply. O A. events B and C O B. events A and C O C. events B and A D. No pairs are dependent. O O O O

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**Title: Understanding Independent and Dependent Events in Probability**

**Introduction:**
When two fair dice are rolled, three events can be defined: 
- Event B: The sum of the dice is odd.
- Event A: The sum of the dice is 7 or more.
- Event C: At least one die shows a 2.

For these events, we examine which pairs are independent and which are dependent.

**Independent Events:**
Events E and F are independent if:
- **Option C:** \( P(E|F) = P(E) \) and \( P(F|E) = P(F) \).

**Questions to Determine Independence:**
- Which pairs of events are independent? Select all that apply:
  - **A.** Events A and C
  - **B.** Events B and C
  - **C.** Events B and A
  - **D.** No pairs are independent

**Dependent Events:**
- Which pairs of events are dependent? Select all that apply:
  - **A.** Events B and C
  - **B.** Events A and C
  - **C.** Events B and A
  - **D.** No pairs are dependent

Understanding and identifying independent and dependent events help in analyzing probabilities effectively, providing insight into real-world scenarios where multiple conditions might influence one another.
Transcribed Image Text:**Title: Understanding Independent and Dependent Events in Probability** **Introduction:** When two fair dice are rolled, three events can be defined: - Event B: The sum of the dice is odd. - Event A: The sum of the dice is 7 or more. - Event C: At least one die shows a 2. For these events, we examine which pairs are independent and which are dependent. **Independent Events:** Events E and F are independent if: - **Option C:** \( P(E|F) = P(E) \) and \( P(F|E) = P(F) \). **Questions to Determine Independence:** - Which pairs of events are independent? Select all that apply: - **A.** Events A and C - **B.** Events B and C - **C.** Events B and A - **D.** No pairs are independent **Dependent Events:** - Which pairs of events are dependent? Select all that apply: - **A.** Events B and C - **B.** Events A and C - **C.** Events B and A - **D.** No pairs are dependent Understanding and identifying independent and dependent events help in analyzing probabilities effectively, providing insight into real-world scenarios where multiple conditions might influence one another.
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