Question

People who hack into computer systems or use someone else’s bank card, through trial and error, will try to figure out the PIN (personal identification number) or password by using personal information. Because PIN numbers must be easily remembered by the person who uses one of these security devices, people often rearrange numbers or letters that are significant to them and use them as a password or PIN. For instance, someone may use the numbers in their birth date as a PIN number. Some will use initials or an important word in their passwords. Answer the following questions about a person who uses significant personal information for their PIN number.

1. If a PIN must be exactly four numbers long, how many possible PIN numbers could a person use?
2. A person decides to use numbers from their date of birth and year of birth in their PIN:

13th of August, 1987

If they use the numbers 13 and 87 in their PIN, how many different PINs could they have? List all the possible PIN numbers by using a tree diagram to organize your counting. The tree diagram has been started for you, but you must complete it.

Be careful. In this situation, each of the numbers will be used only once.

3. Say for instance this person’s PIN is 1387. If a hacker does not know your birth date or does not use your birthday, what is the probability that the hacker will obtain your PIN by chance?
4. If the hacker does know your birth date and decides to use these numbers in various combinations to find your PIN, what is the probability that the hacker will find out your PIN on the first try?
5. What if the person used the month and the year of his/her birth, specifically: 08 for the month and 87 for the year. How many different possible PINs could be used? Use a tree diagram to determine all the possible PINs so that each number is used once, except 8 that must be used twice.
6. If the person’s PIN is 8078, but the hacker does not know any of this information, what is the probability that they will obtain the PIN on the first try?
7. If the hacker does know the birth information and uses these four numbers, what is the probability that the hacker will obtain the PIN on the first try?
8. What do you conclude about the use of personal information to make up the numbers in a PIN? Describe how the knowledge of probability is useful in deciding on a PIN and in protecting personal information through the use of these PINs.

Answer 1

a. 10000, since each of the four numbers can take values from 0 to 9. That is, the pin can be from 0000 to 9999

b. Since 4 distinct numbers can be arranged in 4! = 24 ways, hence there can be 24 different combinations of the PIN

1	3	7	8
1	3	8	7
1	7	3	8
1	7	8	3
1	8	3	7
1	8	7	3
3	1	7	8
3	1	8	7
3	7	1	8
3	7	8	1
3	8	1	7
3	8	7	1
7	1	3	8
7	1	8	3
7	3	1	8
7	3	8	1
7	8	1	3
7	8	3	1
8	1	3	7
8	1	7	3
8	3	1	7
8	3	7	1
8	7	1	3
8	7	3	1

c, Since 10000 PINs are possible, so the probability that the hacker will obtain PIN by chance is 1/10000

d. Since 24 combinations are possible when 4 particular digits are used, hence the probability is 1/24

e. When a number repeats twice, for total permutations we divide 4! by 2! Hence, possible no of PINs when using 0887 are 24/2! = 12

0	7	8	8
0	8	7	8
0	8	8	7
7	0	8	8
7	8	0	8
7	8	8	0
8	0	7	8
8	0	8	7
8	7	0	8
8	7	8	0
8	8	0	7
8	8	7	0

f. Again, since no information is known hence probability is 1/10000

g. Since 12 combinations are possible , hence the probability is 1/12

h. If personal information is used to make a PIN then it becomes much easier to hack the same. Hence, one should never use them to make these sensitive codes. They should be selected randomly so that guessing them is very difficult