11 Alex models the number of goals that a local team will score in any match as follows.
| Number of goals | 0 | 1 | 2 | 3 | 4 | |
| Probability | \(\frac { 3 } { 25 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 8 } { 25 }\) | \(\frac { 7 } { 25 }\) | \(\frac { 2 } { 25 }\) | 0 |
The number of goals scored in any match is independent of the number of goals scored in any other match.
- Alex chooses 3 matches at random. Use the model to determine the probability of each of the following.
- The team will score a total of exactly 1 goal in the 3 matches.
- The numbers of goals scored in the first 2 of the 3 matches will be equal, but the number of goals scored in the 3rd match will be different.
During the first 10 matches this season, the team scores a total of 31 goals.
- Without carrying out a formal test, explain briefly whether this casts doubt on the validity of Alex's model.
\section*{END OF QUESTION PAPER}