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Sagot :
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:
[tex]\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)\times P(2)=0.45\times0.45=0.2025 \\ \\ \therefore\text{probability of the team winning by going for 2 points twice=} \\ 0.2025\times100\text{ \%} \\ =20.25\text{ \%} \end{gathered}[/tex]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
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