Person A and Person B each have four cards, with each card labeled with a number. Person A's cards are labeled with the numbers 1, 3, 5, 7, and Person B's cards are labeled with the numbers 2, 4, 6, 8. They play four rounds of competition. In each round, both players randomly select one card from their own cards and compare the numbers. The player with the larger number scores 1 point, and the player with the smaller number scores 0 points. Then each player discards the card used in that round (discarded cards cannot be used in subsequent rounds). The probability that Person A's total score after four rounds is at least 2 is $\_\_\_\_$ .
Person A and Person B each have four cards, with each card labeled with a number. Person A's cards are labeled with the numbers 1, 3, 5, 7, and Person B's cards are labeled with the numbers 2, 4, 6, 8. They play four rounds of competition. In each round, both players randomly select one card from their own cards and compare the numbers. The player with the larger number scores 1 point, and the player with the smaller number scores 0 points. Then each player discards the card used in that round (discarded cards cannot be used in subsequent rounds). The probability that Person A's total score after four rounds is at least 2 is $\_\_\_\_$ .