Probability team A beats team B after penalty (5 kicks)

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marthehjallis

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Hi, I'm struggling with a task, and could really use some help. It's statistics and probabilities for engineers and scientists.

The task:
In a penalty-competition between team A and team B, both teams starts off with 5 penalty-kicks each. Let X tell us the number of scored goals for team A, and let Y tell us the number of scored goals for team B. We assume that X~bin(5,0.8) and Y~bin(5,0.75). We assume that the two teams scores independently of each other.
What is the probability that team A has won the penalty-competition after 5 kicks has been kicked by each team?

Thank you in advance for any eventual reply :)
 
marthehjallis said:
Hi, I'm struggling with a task, and could really use some help. It's statistics and probabilities for engineers and scientists.

The task:
In a penalty-competition between team A and team B, both teams starts off with 5 penalty-kicks each. Let X tell us the number of scored goals for team A, and let Y tell us the number of scored goals for team B. We assume that X~bin(5,0.8) and Y~bin(5,0.75). We assume that the two teams scores independently of each other.
What is the probability that team A has won the penalty-competition after 5 kicks has been kicked by each team?

Thank you in advance for any eventual reply :)
Click to expand...
We're interested in finding the [imath]\Pr(X>Y)[/imath]. To start, list all the possible ways that [imath]X>Y[/imath].
Hint: There are 15 combinations.
 
Last edited:
marthehjallis said:
Hi, I'm struggling with a task, and could really use some help. It's statistics and probabilities for engineers and scientists.

The task:
In a penalty-competition between team A and team B, both teams starts off with 5 penalty-kicks each. Let X tell us the number of scored goals for team A, and let Y tell us the number of scored goals for team B. We assume that X~bin(5,0.8) and Y~bin(5,0.75). We assume that the two teams scores independently of each other.
What is the probability that team A has won the penalty-competition after 5 kicks has been kicked by each team?

Thank you in advance for any eventual reply :)
Click to expand...
marthehjallis said:
What is the probability that team A has won the penalty-competition after 5 kicks has been kicked by each team?
Click to expand...
For that to happen, A & B must have missed 4 penalty kicks.

Then A scores on the 5th one and B misses yet the fifth one.
 
Subhotosh Khan said:
For that to happen, A & B must have missed 4 penalty kicks.

Then A scores on the 5th one and B misses yet the fifth one.
Click to expand...
From what I understand, the OP is describing a penalty kick shootout.
From Wikipedia:
"In a penalty shoot-out, each team takes turns shooting at goal from the penalty mark, with the goal defended only by the opposing team's goalkeeper. Each team has five shots which must be taken by different kickers; the team that makes more successful kicks is declared the victor."
 
BigBeachBanana said:
From what I understand, the OP is describing a penalty kick shootout.
From Wikipedia:
"In a penalty shoot-out, each team takes turns shooting at goal from the penalty mark, with the goal defended only by the opposing team's goalkeeper. Each team has five shots which must be taken by different kickers; the team that makes more successful kicks is declared the victor."
Click to expand...
Right - the other scenario could be that A and B are tied after 4 shots each (1-1 or 2-2 or 3-3 or 4-4) and 5 th shots will decide the game.
 
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