China Naming Network - Naming consultation - Someone has a string of eight keys with the same shape, and only one key can open the door. The probability from eight keys at a time to randomly opening the door for the third time.
Someone has a string of eight keys with the same shape, and only one key can open the door. The probability from eight keys at a time to randomly opening the door for the third time.
We can imagine the problem as two steps.
Step 1: Arrange 8 keys in sequence;
Step 2: Take out the eight handles in turn and open the door until it opens.
So the probability of opening the door for the third time is the probability of finding the key in the third place in the first step.
Because all the keys are the same, there is no difference.
So the probability of putting the key anywhere is 1/8.
So not only the probability of the third opening is 1/8, but also the probability of any opening is 1/8.