7.5. Sums and Differences of Independent Random Variables http://www.ck12.org
These probabilities are added because the outcomes are disjoint.
Example:
The Quebec Junior Major Hockey League has five teams from the Maritime Provinces. These teams are Cape Breton
Screaming Eagles, Halifax Mooseheads, PEI Rockets, Moncton Wildcats and Saint John Sea Dogs. Each team has
its own hometown arena and each arena has a seating capacity that is listed below:
TABLE7.12:
Team Seating Capacity (Thousands)
Screaming Eagles 5
Mooseheads 10
Rockets 4
Wildcats 7
Sea Dogs 6A schedule can now be drawn up for the teams to play pre-season exhibition games. One game will be played in
each home arena and the possible capacity attendance will also be calculated. In addition, the probability of the total
possible attendance being at least 12,000 people will also be calculated.
The number of possible combinations of two teams from these five is 10. ( 5 C 2 ). The following table shows the
possible attendance for each of the pre-season, exhibition games.
TABLE7.13:
Teams Combined Attendance Capacity for Both Games
(Thousands)
Eagles/Mooseheads 5 + 10 = 15
Eagles/Rockets 5 + 4 = 9
Eagles/Wildcats 5 + 7 = 12
Eagles/Sea Dogs 5 + 6 = 11
Mooseheads/Rockets 10 + 4 = 14
Mooseheads/Wildcats 10 + 7 = 17
Mooseheads/Sea Dogs 10 + 6 = 16
Rockets/Wildcats 4 + 7 = 11
Rockets/Sea Dog 4 + 6 = 10
Sea Dogs/Wildcats 6 + 7 = 13The last calculation is to determine the probability distribution of the capacity attendance.
TABLE7.14:
Capacity Attendance,x Probability,p
9 0. 1
10 0. 1
11 0. 2
12 0. 1
13 0. 1
14 0. 1
15 0. 1
16 0. 1
17 0. 1