A programmer is about to attempt to compile a series of 11 similar programs. Let Ai be the event that the ith program compiles successfully for i = 1, . . . , 11.When the programming task is easy, the programmer expects that 80 percent of programs should compile. When the programming task is difficult, she expects that only 40 percent of the programs will compile. Let B be the event that the programming task was easy. The programmer believes that the events A1, . . . ,A11 are conditionally independent given B and given Bc.
a. Compute the probability that exactly 8 out of 11 programs will compile given B.
b. Compute the probability that exactly 8 out of 11 programs will compile given Bc.