In the last minute of Super Bowl XLIX the Seattle Seahawks w

In the last minute of Super Bowl XLIX, the Seattle Seahawks, who are behind by four points,
must decide whether to run or pass. To simplify, suppose that in each case, there are three
mutually exclusive outcomes: a touchdown, no gain, and turnover.
If the Seahawks run, the probabilities of each outcome are:

Solution

a) Seahawks decide to run

prob

Win prob

Joint prob

Touchdown

60%

95%

57%

Nogain

31%

80%

31.20%

Turnover

4%

0

0

Total

81.20%

Prob they win = 0.8120

b) Seahawks decide to pass.

prob

Win prob

Joint prob

Touchdown

65%

95%

61.75%

Nogain

31%

80%

24.80%

Turnover

4%

0

0

Total

86.55%

Prob they win = 0.8655

c) Decide to pass as prob is more for winning.