Question

1. Your I-phone has a numeric passcode to press to access it. This code consists of 4 numbers. If someone tries the codes and gets them incorrect, the phone will shut down after three incorrect attempts. What is the probability that a person who is just guessing the code will get it correct within three guesses (hint…how does this compare to the probability of not getting it right in three attempts)? also How does the situation (and probability) change with the I phone if the passcode is 6 digits?

Answer 1

Total number of codes possible

= 10*10*10*10 = 10000 as there are 10 possible digits for each of the 4 characters of the code. Therefore there must be 999 incorrect codes and 1 correct code.

Now probability that the person gets the correct code within 3 tries is computed here as:
= 1 - Probability that all 3 tries are incorrect codes.

= 1 - ( Number of ways to select 3 codes from 999 incorrect ones / Total ways to select 3 codes from 1000 codes)

Therefore 0.003 is the required probability here.

Now for a 6 digit code, the same probability is computed here as:

Therefore 0.000003 is the required probability here.