Respuesta :
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 = [tex]10^4 =10000[/tex]
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
= [tex]\frac{1}{10000} +\frac{9999}{10000}\frac{1}{10000}+(\frac{9999}{10000})^2\frac{1}{10000}[/tex]
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
The probability that you get in (without letting off the alarm) is 0.000992.
- The calculation is as follows:
= Probability of the correct code on the first attempt + Probability of the correct code on the second attempt + Probability of the correct code on the third attempt
[tex]=\frac{1}{9\times8\times7\times6} + \frac{(9\times8\times7\times6)-1}{9\times8\times7\times6} \times \frac{1}{(9\times8\times7\times6)-1} + \frac{(9\times8\times7\times6)-1}{9\times8\times7\times6} \times \frac{(9\times8\times7\times6)-2}{(9\times8\times7\times6)-1} \times \frac{1}{(9\times8\times7\times6)-2}\\\\ = \frac{3}{9\times8\times7\times6} \\\\= \frac{1}{1008} \\\\[/tex]
= 0.000992
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