# Bar-eli, Azar, Ritov, Keidar-Levin, and Schein (2007) analyzed 286 penalty kicks among professional soccer players. They recorded the direction that the ball was kicked (left, center, right) and the direction that the goalie went to block the kick (left, center, right). The table shows the results of their study.

Bar-eli, Azar, Ritov, Keidar-Levin, and Schein (2007) analyzed 286 penalty kicks among professional soccer players. They recorded the direction that the ball was kicked (left, center, right) and the direction that the goalie went to block the kick (left, center, right). The table shows the results of their study.
Jump direction Left Center Right Total Kick
direction Left 54 1 37 92 Center 41 10 31 82 Right 46 7 59 112 Total 141 18 127 286
(a) What is the probability that the ball was kicked to the left?
(b) What is the probability that the ball was kicked left and the goalie jumped left?
(c) What is the probability that the goalie jumped to the left, given that the ball was kicked to the left? Note: This is now a conditional probability statement.

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