To evaluate the technical support from a computer manufacturer, the number of rings before a call is answered by a service representative is tracked. Historically, 70% of the calls are answered in two rings or less, 25% are answered in three or four rings, and the remaining calls require five rings or more. Suppose that you call this manufacturer 10 times and assume that the calls are independent. 

(a) What is the probability that eight calls are answered in two rings or less, one call is answered in three or four rings, and one call requires five rings or more?

(b) What is the probability that all 10 calls are answered in four rings or less?

(c) What is the expected number of calls answered in four rings or less?

(d) What is the conditional distribution of the number of calls requiring five rings or more given that eight calls are answered in two rings or less?

(e) What is the conditional expected number of calls requiring five rings or more given that eight calls are answered in two rings or less?

(f) Is the number of calls answered in two rings or less and the number of calls requiring five rings or more independent random variables?