Name: Karen

Who is asking: Student
Level: All

Question:
it is about probability!
Q : A man has a bunch of three keys, only one of which fits the lock of his front door.
When he comes home in the dark he tries the keys at random until he finds the one fits. Find the probability that in a week of five nights, he tries the right key first on at least one night.

Hi Karen,
I'll give you a suggestion that should help you get started.

To do this problem directly you need to find five probabilities and add them.

  the probability that he tries the right key first on exaclty one night,
  the probability that he tries the right key first on exaclty two nights,
  the probability that he tries the right key first on exaclty three nights,
  the probability that he tries the right key first on exaclty four nights,
  the probability that he tries the right key first on exaclty five night,

It is easier to ask "What is the probability that he tries the right key first on exaclty zero nights?" What you want is then one minus this probability.

Cheers
Penny