Dr. Emmett Brown has a large stockpile of flux capacitors, 15% of which are in need of repair. He is equipped with only 4 repair kits, and selects flux capacitors one at a time to test. Suppose that, if a flux capacitor is working, it takes 10 minutes to test, and that if it is in need of repair, it takes 30 minutes to both test and repair.
(Assume that by "large" stockpile, that there are infinite flux capacitors to test.)
Q: What is the expectation and variance of the time it takes until Dr. Emmett Brown is out of repair kits? (i.e. Dr. Brown has encountered and repaired 4 flux capacitors)