Question

A lock on a lab door has buttons numbered 0 through 9. The right code for opening the lock is 8542. Also, if on three consecutive attempts, a wrong code (a code is a combination of 4 ordered distinct digits) is entered, then a burglar alarm is let off. You forgot the right code, but remember that the code consists of 4 distinct digits. So you keep on trying one code after another without replacement. Compute the probability that you get in (without letting off the alarm).

Answer 1

Probability that we get in without letting the alarm go on is computed as:

= Probability that we get the correct code on the first attempt + Probability that we get the correct code on the second attempt + Probability that we got the correct code on the third attempt

Therefore 0.000992 is the required probability here.