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 following table shows the results of their study.

Based on this table,
(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?

Transcribed Image Text:

Jump direction Left Center Right Total 92 10 อา 02 Right 46 7 50 112 Left 54 37 Kick direction Center 41 286 18 Tota 14 B 127