<PRE><B>Question 1200769</B>
**1. Define Probabilities:**

* **wA:** Probability of winning against A = 1 - pA = 1 - 0.47 = 0.53
* **wB:** Probability of winning against B = 1 - pB = 1 - 0.53 = 0.47

**2. Calculate Probabilities for Each Order:**

* **ABA Order:**
    * **Winning Scenario:** Win A, Win B, Win/Lose A
    * Probability: wA * wB * (wA + pA) = 0.53 * 0.47 * (0.53 + 0.47) = 0.2491

* **BAB Order:**
    * **Winning Scenario:** Win B, Win A, Win/Lose B
    * Probability: wB * wA * (wB + pB) = 0.47 * 0.53 * (0.47 + 0.53) = 0.2491

**3. Conclusion:**

* The probability of winning with the ABA order is 0.2491.
* The probability of winning with the BAB order is 0.2491.

**Therefore, both orders have the same probability of winning.**
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