L = the event that the goalkeeper jumps to the left C = the event that the goalkeeper stays in the center R = the event that the goalkeeper jumps to the right B = the event that the penalty kick is blocked Based on their analysis of the penalty kicks, the authors of the paper found the following probabilities: P(B | L) = 0.142 P(B | C) = 0.333 P(B | R) = 0.126 P(L) = 0.493 P(C) = 0.063 P(R) = 0.444 a) Draw a tree diagram that captures the information and probabilities given above. You must correctly label all outcomes, the probabilities for the branches, and the probabilities for the final outcomes.
The paper “Action Bias among Elite Soccer Goalkeepers: The case of Penalty Kicks” (Journal of Economic Psychology [2007}: 606-621) presents an analysis of 286 penalty kicks in televised championship soccer games from around the world. In a penalty kick, the only players involved are the kicker and the goalkeeper from the opposing team. The kicker tries to kick a ball into the goal from a point located 11 meters away. The goalkeeper tries to block the ball from reaching the goal. For each penalty kick analyzed, the researchers recorded the direction that the goalkeeper moved (jumped to the left, stayed in the center, or jumped to the right) and whether or not the penalty kick was successfully blocked.
Consider the following events:
L = the
Based on their analysis of the penalty kicks, the authors of the paper found the following probabilities:
P(B | L) = 0.142 P(B | C) = 0.333 P(B | R) = 0.126 P(L) = 0.493 P(C) = 0.063 P(R) = 0.444
a) Draw a tree diagram that captures the information and probabilities given above. You must correctly label all outcomes, the probabilities for the branches, and the probabilities for the final outcomes.
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