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Can you help me draw the tree diagram and association calculations please.

A firm has two photocopying

machines. The old one is available for use 80% of

the time and the new one 90% of the time. The machine availabilities are

independent of one another.

a. Construct a tree diagram to display the above information.

b. Determine the probability that at a randomly selected time:

i. both machines are available, ii neither machine is available

iii. exactly one machine is available, iv. at least one machine is available

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