Hi all,
So I have this assignment due for my statistics class due in 2 days and I'm completely stuck on how to do one of the problems (plus I just want to be able to verify my answers for the other 2 parts of that question). IF anyone can help me out, I would greatly appreciate it.
4. A software development firm has two programmers, Alice and Jill, to whom they assign software projects at random, with equal probabilities. Alice is a rather good programmer. Half the time, her programs have no bugs, and otherwise they have just a single bug. Jill isn't as good. She has an equal chance of producing a program with no bug, one bug, two bugs, three bugs, or four bugs (essentially, each of these possibilities has probability 1/5). After Alice or Jill finish a program, it is sent to the testing department, where they try to find the bugs. The testers have a 1/3 chance of finding each bug, and whether they find one bug is independent of whether they find any other bug (so the events of them finding each bug are mutually independent).
a) What is the expected number of bugs in a program (which might be written by either Alice or Jill) that is sent to the testers?
b) What is the expected number of bugs in a program that are not found by the testers?
c) Suppose the testers find exactly one bug in a program. What is the probability that there are no more bugs in this program? What is the probability that this program was written by Alice?
For part a) I got 5/4
For part b) I got 5/6
However, I am completely stuck on part c) (and I want to just be able to verify my answer for a and b). Any and all help would be appreciated.
I am going to sleep. But will check back in the morning!
Again, thanks in advance for any help you can offer.
So I have this assignment due for my statistics class due in 2 days and I'm completely stuck on how to do one of the problems (plus I just want to be able to verify my answers for the other 2 parts of that question). IF anyone can help me out, I would greatly appreciate it.
4. A software development firm has two programmers, Alice and Jill, to whom they assign software projects at random, with equal probabilities. Alice is a rather good programmer. Half the time, her programs have no bugs, and otherwise they have just a single bug. Jill isn't as good. She has an equal chance of producing a program with no bug, one bug, two bugs, three bugs, or four bugs (essentially, each of these possibilities has probability 1/5). After Alice or Jill finish a program, it is sent to the testing department, where they try to find the bugs. The testers have a 1/3 chance of finding each bug, and whether they find one bug is independent of whether they find any other bug (so the events of them finding each bug are mutually independent).
a) What is the expected number of bugs in a program (which might be written by either Alice or Jill) that is sent to the testers?
b) What is the expected number of bugs in a program that are not found by the testers?
c) Suppose the testers find exactly one bug in a program. What is the probability that there are no more bugs in this program? What is the probability that this program was written by Alice?
For part a) I got 5/4
For part b) I got 5/6
However, I am completely stuck on part c) (and I want to just be able to verify my answer for a and b). Any and all help would be appreciated.
I am going to sleep. But will check back in the morning!
Again, thanks in advance for any help you can offer.
