Question

A football team is losing by 14 points near the end of a game. The team scores two touchdowns (worth 6 points each) before the end of the game. After each touchdown, the coach must decide whether to go for 1 point with a kick (which is successful 99% of the time) or 2 points with a run or pass (which is successful 45% of the time). If the team goes for 1 point after each touchdown, what is the probability that the coach’s team wins? loses? ties? If the team goes for 2 points after each touchdown, what is the probability that the coach’s team wins? loses? ties?

Answer 1

From the question, there are some scenarios we need to cater for:

- The team is down 14 points.

- It is a given that the team scores 2 touchdowns whatever the case. This means the team has 12 points in the bag.

- That leaves 2 points to overturn the loss, or draw or lose

If the team wins:

The team can only win if they score their 2 points runs twice. i.e. An increase in 4 points from the two plays would overturn the score and the team would lead the game by 2 points.

The question asks us to find the probability of the team winning if the team goes for 2 points after each 6-point touchdown.

We can solve this as:

`\begin{gathered} \text{Probability of scoring 2 =} \\ P(2)=45\text{ \%=0.45} \\ \\ \therefore\text{Probability of scoring 2 the first time AND Probability of scoring 2 the second time=} \\ P(2)* P(2)=0.45*0.45=0.2025 \\ \\ \therefore\text{probability of the team winning by going for 2 points twice=} \\ 0.2025*100\text{ \%} \\ =20.25\text{ \%} \end{gathered}`

If the team loses:

If the team loses, there are some scenarios to take into consideration:

1. If the team tries 1 point plays and succeeds one time and failing the other time

2. If the team tries 1 point plays and fails twice.

3. If the team tries 2 point plays and they fail twice. (i.e. if they succeed even once, they can draw the match