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Two football teams, A and B, are set to compete in two matches. The outcomes of these matches are independent. The probabilities of team A winning, tying, or losing a match against team B are 1/2, 1/6, and 1/3, respectively. Teams earn 3 points for a win, 1 point for a tie, and 0 points for a loss. Let the total points scored by teams A and B after both matches be represented by P_A and P_B, respectively. What is the probability that P_A exceeds P_B?
- 1/4
- 5/12
- 1/2
- 7/27
Correct answer: 5/12
Solution
The probability that P_A exceeds P_B is 5/12, which is calculated by considering the possible outcomes of the two matches and their corresponding probabilities.
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