A paper presents an interesting analysis of 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 entering 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 event that the goalkeeper jumps to the leftC = the event that the goalkeeper stays in the centerR = the event that the goalkeeper jumps to the rightB = the event that the penalty kick is blockedBased on their analysis of the penalty kicks, the authors of the paper gave the following probability estimates.P(L) = 0.463P(B|L) = 0.142 P(C) = 0.123P(B|C) = 0.333 P(R) = 0.414P(B|R) = 0.126 (b)Use the given probabilities to construct a hypothetical 1,000 table with columns corresponding to whether or not a penalty kick was blocked and rows corresponding to whether the goalkeeper jumped left, stayed in the center, or jumped right. (Round your answers to the nearest integer.) Use the table to calculate the probability that a penalty kick is blocked.

Given information: The events corresponding to the given scenario are as follows: L = the…

Answered: A paper presents an interesting…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 17E

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A paper presents an interesting analysis of 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 entering 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 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 gave the following probability estimates.

P(L)	=	0.463
P(B\|L)	=	0.142

P(C)	=	0.123
P(B\|C)	=	0.333

P(R)	=	0.414
P(B\|R)	=	0.126

(b)

Use the given probabilities to construct a hypothetical 1,000 table with columns corresponding to whether or not a penalty kick was blocked and rows corresponding to whether the goalkeeper jumped left, stayed in the center, or jumped right. (Round your answers to the nearest integer.)

Use the table to calculate the probability that a penalty kick is blocked.

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