SOLUTION: An absent minded professor has five keys in his pocket, only one of which will open his front door. He randomly takes a key from his pocket, tries it, and if it fails puts it back

Question 1088142: An absent minded professor has five keys in his pocket, only one of which will open his front door. He randomly takes a key from his pocket, tries it, and if it fails puts it back in his pocket.
a. Whats the probability after four tries the door is still locked?
b. The professors wife suggests it may be smarter to lay aside the keys that havent fit so far. What would be the probability if the professor follows his wifes strategy?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is a geometric function: (1-p)^4 would be the probability that after 4 tries, the door would be locked, and that is 0.8^4=0.4096.
Not working would be (4/5)^4
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(4/5)(3/4)(2/3)(1/2) is the probability that it would be locked given that the sampling is doe without replacement. This is 24/120=0.2
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