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The probabilities of X, Y, and Z becoming managers are 4/9, 2/9 and 1/3 respectively. The probabilities that the bonus scheme will be introduced if

The probabilities of X, Y, and Z becoming managers are 4/9, 2/9 and 1/3 respectively. The probabilities that the bonus scheme will be introduced if X,Y, and Z become managers are 3/10, 1/2 and 4/5 respectively. If the bonus scheme is introduced, what is the probability that X is the manager?

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