A woman has seven keys on a key ring, one of which fits the door she wants to un

Question

A woman has seven keys on a key ring, one of which fits the door she wants to unlock. She randomly selects a key and tries it. If it does not unlock the door, she randomly selects another key from those remaining and tries to unlock the door with it. She continues in this manner until the door is unlocked. Let X be the number of keys she tries before unlocking the door, counting the key that actually worked. Find the probability function of X.

I know that the answer is:

How can I arrive at this answer?

Please show your work!! Thank you.

Explanation / Answer

Required probability function of X

If X=1 then probability =(1C1)/(1C1)=1.

If X=2 then probability =(1C1)/(2C1)=1/2.

If X=3 then probability =(1C1)/(3C1)=1/3. ...........

If X=7 then probability =(1C1)/(7C1)=1/7.

So P(X=x)=(1/n) ,x=1,2,3,....,n.

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