A Firm has two photocopying machines. The old one is available for use 80% of the time and the new one is available for use 91% of the time. The machine availabilities are independent of each other.

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

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

i) Both machines are available.

ii) neither is available.

iii) exactly one is available.

iv) atleast one machine is available.