A and B are soccer teams involved in a shootout. Each team chooses 2 players and

Question

A and B are soccer teams involved in a shootout. Each team chooses 2 players and each player takes a penalty shot. A team wins in the first phase if they score more total goals. If the score is tied, they move on to a second phase. Suppose the probability that the players will score are: for A .8 and .8; for B .9 and .7

Let’s look at the first phase.

a) Find the probability that team A scores 0, 1, or 2 goals.
b) Find the probability that team B scores 0, 1, or 2 goals.
c) Find the probability that team A wins in the first phase.
d) Find the probability that the teams are tied after the first phase.

Now let’s look at cases where the teams move on to the second phase: in this phase each team chooses their best player and a round consists of each player taking one shot. A team wins if they score and the other team does not; otherwise they go to another round (using the same player). Play continues until a team wins.

e) Find the probability that team A wins if it goes to the second phase.
f ) Find the probability that team A wins in total.
g) Find P(A wins) if the teams continue with both their players in the second phase.

I have the answers for a, b, c, and d. I just need e, f, and g.

Explanation / Answer

The second phase comes when the goal is equal.

A wins if they score the goal but other team doesnot goal that means

p1 is the score the goal by team A and p2 is the score the goal by team B

e) Then, the probability that team A wins if it goes to the second phase is

p1q2 + q1p1q22 +,,,,,,

f) the probability that team A wins in total is

The sum of phase first and the second phase.

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