2022 ASRJC P2 Q6

In a soccer practice, the coach instructs the players to practise their penalty kicks. A player scores if he successfully kicks a ball into the net of a goal post. The probability that a player scores on the first kick is \(\frac{2}{5}\). For all the subsequent kicks, the probability of scoring on that kick will be \(\frac{4}{5}\) if the player scores in the preceding kick, and the probability of scoring on that kick will be \(\frac{1}{6}\) if the player did not score in the preceding kick.

1. Owen kicked the ball three times consecutively for his practice. Find the probability that he scored on the third kick, given that he scored only twice out of the three kicks.[3]
2. Three players each kicked the ball four times consecutively for their practices. Find the probability that one of the players scored on all four kicks, another player scored on the first kick only, while the remaining player only scored on the second and third kicks.[3]