A Contractor has two subcontractors for his excavation work

A Contractor has two subcontractors for his excavation work. Experience shows that in 60% of the time, subcontractor A was available to dojob, whereas subcontractor B was available 90% of the time. Also, the contractor is able to get at least one of these two subcontractors 90% of the time.job, whereas subcontractor B was available 90% of the time. Also, the contractor is able to get at least one of these two subcontractors 90% of the time.

a) What is the probability that both subcontractors will be available to do the next job?

b) If the contractor learned that subcontractor A is not available for the job, what is the probability that the other subcontractor will be available?

c) Let Ea denote the event that subcontractor A is available and Eb denotes the event that subcontractor B is available,

i) Are Ea and Eb statistically independent?

ii) Are Ea and Eb mutually exclusive?

iii) Are Ea and Eb collectively exhaustive?