Aman has n keys on a key ring, one of which opens the door to his apartment. having celebrated a bit too much one evening, he returns home only to find himself unable to distinguish one key from another. resourceful, he works out a fiendishly clever plan: he will choose a key at random and try it. if it fails to open the door, he will discard it and choose at random one of the remaining n−1 keys, and so on. clearly, the probability that he gains entrance with the first key he selects is 1/n. show that the probability the door opens with the third key he tries is also 1/n.

Xinhong company is considering replacing one of its manufacturing machines. the machine has a book value of $39,000 and a remaining useful life of 5 years, at which time its salvage value will be zero. it has a current market value of $49,000. variable manufacturing costs are $33,300 per year for this machine. information on two alternative replacement machines follows. alternative a alternative b cost $ 115,000 $ 117,000 variable manufacturing costs per year 22,900 10,100 1. calculate the total change in net income if alternative a and b is adopted. 2. should xinhong keep or replace its manufacturing machine