Question

Q. I face the following problem every single day. I have three keys that look like each other but only one of them opens the door of my office.

i) Let’s say I randomly plug in one of these three keys. What is the probability that it will open my door?

ii) What is probability that I will be able to enter my office in my next attempt given that the first key did not open my door? Please answer this question under the following two different scenarios:

ii.a) The first key didn’t open the door but at least I paid attention to it & marked the key that didn’t work.

ii.b) The first key didn’t open the door but unfortunately I forgot to exclude it and accidentally, put it back next to the others.

iii) How many attempts would it be expected for me to open my office door if I am a reasonable person?

iv) How many attempts would it be expected for me to open my office door if I am a forgetful/ memoryless person?

Please show work.

Answer 1