a) To create an organized list, we can start with the number of wins and find all possible combinations of ties and losses that would result in 29 points:
- 1 win: 24 losses or 22 losses and 1 tie or 20 losses and 2 ties or 18 losses and 3 ties or 16 losses and 4 ties or 14 losses and 5 ties or 12 losses and 6 ties or 10 losses and 7 ties or 8 losses and 8 ties or 6 losses and 9 ties or 4 losses and 10 ties or 2 losses and 11 ties or 13 ties
- 2 wins: 19 losses or 17 losses and 1 tie or 15 losses and 2 ties or 13 losses and 3 ties or 11 losses and 4 ties or 9 losses and 5 ties or 7 losses and 6 ties or 5 losses and 7 ties or 3 losses and 8 ties or 1 loss and 9 ties
- 3 wins: 14 losses or 12 losses and 1 tie or 10 losses and 2 ties or 8 losses and 3 ties or 6 losses and 4 ties or 4 losses and 5 ties or 2 losses and 6 ties or 7 ties
- 4 wins: 9 losses or 7 losses and 1 tie or 5 losses and 2 ties or 3 losses and 3 ties or 1 loss and 4 ties
- 5 wins: 4 losses or 2 losses and 1 tie or 1 loss and 2 ties
b) To find the probability that Nathan's team had more losses than ties, we need to count the number of combinations where the number of losses is greater than the number of ties. From the list above, we can see that there are 28 such combinations (all except the one with 13 ties). To find the probability, we need to divide the number of favorable outcomes by the total number of outcomes:
Probability = 28 / 64 = 0.44
So the probability that Nathan's team had more losses than ties is 0.44, or 44%.