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The probability that Sam is coaching a game is \(\frac{6}{10}\), and the probability that Alex is coaching is \(\frac{4}{10}\).
With Coach Sam, the probability of being Goalkeeper is \(\frac{1}{2}\).
With Coach Alex, the probability of being Goalkeeper is \(\frac{2}{3}\).
Let \(S\) be the event that Sam is the coach.
Let \(G\) be the event of being the goalkeeper.
Choose the correct probability tree diagram:
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