Question

The table summarizes the scoring of a football game between Team A and Team B. A touchdown (TD) is worth 6 points, a field goal (FG) is worth 3 points, a safety (S) is worth 2 points, and a point after touchdown (PAT) is worth 1 point. Use matrix multiplication to find the final score.
TD FG S PAT
Team A 5 4 0 4
Team B 3 3 1 2

Answer 1

Answer:

To score 5 points, team A need to win 2 matches and draw 1 match.

Let W be the event that team A wins the game.

Let D be the event that team A draws the game.

To score 5 points, possible outcomes of 3 matches are WWD,WDW,DWW

Probability to score 5 points =P(WWD)+P(WDW)+P(DWW)

=P(W)P(W)P(D)+P(W)P(D)P(W)+P(D)P(W)P(W) ...(W and D are independent events)

=(

3

1

×

3

1

×

6

1

)+(

3

1

×

6

1

×

3

1

)+(

6

1

×

3

1

×

3

1

)

=

18

1