4 Answer part (i) of this question on the insert provided. Mancaster Hockey Club invite prospective new players to take part in a series of three trial games. At the end of each game the performance of each player is assessed as pass or fail. Players who achieve a pass in all three games are invited to join the first team squad. Players who achieve a pass in two games are invited to join the second team squad. Players who fail in two games are asked to leave. This may happen after two games.

• The probability of passing the first game is 0.9
• Players who pass any game have probability 0.9 of passing the next game
• Players who fail any game have probability 0.5 of failing the next game
  1. On the insert, complete the tree diagram which illustrates the information above.
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  2. Find the probability that a randomly selected player
     (A) is invited to join the first team squad,
     (B) is invited to join the second team squad.
  3. Hence write down the probability that a randomly selected player is asked to leave.
  4. Find the probability that a randomly selected player is asked to leave after two games, given that the player is asked to leave.

Angela, Bryony and Shareen attend the trials at the same time. Assuming their performances are independent, find the probability that

at least one of the three is asked to leave,

they pass a total of 7 games between them.