A machine makes errors in a certain operation with probability p. There are two types of errors: type A error and type B error. The fraction of errors of type A is a, and the fraction of errors of type B is 1a.
a. What is the probability of k errors in n operations?
b. What is the probability of kA type A errors in n operations?
c. What is the probability of kB type B errors in n operations?
d. What is the probability of kA type A errors and kB type B errors in n operations?