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

Answer:

Step-by-step explanation:

given that 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.

when you forget the code, you try at random

There are 10 ways of selecting each digit

So total number of ways of trials at random = $10^4 =10000$

The probability that you get in (without letting off the alarm).

= Probability that you try correct number in I or II or III trial atmost

Prob for correct guessing = 1/10000

The probability that you get in (without letting off the alarm).

= Probability that you try correct number in I or II or III trial atmost

= $\frac{1}{10000} +\frac{9999}{10000}\frac{1}{10000}+(\frac{9999}{10000})^2\frac{1}{10000}$

Because if you get in I trial you leave.  If you fail in I you try for second, similarly if you fail 2 times 3rd should be correct

=0.0002