Question

To fully take advantage of Lionel Messi’s dribbling skill, Barcelona is working on a new team tactic in order to create more one-on-one chances for Messi. Suppose that before implementing the new tactic the number of one-on-one chances Messi has in a soccer game is a Poisson random variable with parameter λ 5. If the team successfully applies the new tactic, it will increase the Poisson parameter to λ 7. Since it is still a new tactic and the team needs more time to fully master it, it is expected to work for 60% games in the first half of the season. If in the match against Real Madrid Messi had 9 one-on-one chances, how likely is it that Barcelona was able to make use of the new tactic in that game?

Answer 1

We are required to find P[Barcelona was able to make use of the new tactic|Messi had 9 one-on-one chances]

Let X denote the event that Barcelona was able to make use of the new tactic. P[X]=0.6

Let Y denote the number of one-on-one chances that Messi has during a game, where Y follows Pois(\lambda)

Therefore, we need P[X|Y=9]

It is seems Barcelona was (~)81% likely to make use of the new tactic in the game.