1. ## Probability Question

I'm having a hard time figuring this out and setting it up. I get really confused with symbols and how to write the problems out.

Ok a football team needs to score 23 points in three plays. Assuming they're definitely scoring 3 touchdowns they still need 5 points. A field goal has a probability of 82% success rate. A 2 point conversion 18% probability of success.
Is it better to go for three 2 point or Two 2 point conversions and one field goal and whether they should start with the fg followed by two 2pt conversions or 2 pt conversions first and then a fg.

2. ## Re: Probability Question

Outcomes yielding success:
2pt + 2pt + 2pt
2pt + 2pt + 1pt
2pt + 1pt + 2pt
1pt + 2pt + 2pt

Probability of success in each case:
$(.18)^3 = .005832$
$(.18)^2(.82) = .026568$
$(.18)(.82)(.18) = .026568$
$(.82)(.18)^2 = .026568$

So, it does not matter from a probability standpoint. They have the best chance of making the 23 points if they kick one field goal. It would be different if they could make up extra points somehow. I'd say, go for the most difficult first. If you fail the first 2-pt conversion, there is no point in trying for the 23 points anymore, and you may as well kick the field goal for the next two touchdowns (increase your Expected Value for total points).

3. ## Re: Probability Question

It seems as though the way your explaining it is comparable to what I am covering in my class in class we go over it as nCr. Then p and q also come into the equation.