I came across this problem during our maths class at the university. I am having trouble formulating this problem (wondering if my approach is correct). Am I supposed to use Binomial distribution? I am unable to find the system anywhere.
Suppose that penalty conversion probability for the players of Italy and England are as follows:
Probability of player scoring a penalty
What is the chance of England scoring less than three penalties in the shootout?
What is the chance of Italy scoring three or more penalties?
I just need a hint about the first question (England), and that'd be enough, I believe, for me to be able to solve this.
Thanks a lot in advance.