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# What is the probability of getting a license plate that has a repeated letter or digit if you live in a state that has two numerals followed by two letters followed by four numerals?

Updated: 12/23/2022

Wiki User

13y ago

There are ten digits and twenty-six letters, assuming unconstrained choice of both. The probability of getting a repetition in the first two digits is 10/100, since there are 10 repetitious combinations of two digits among the 100 pairs of digits possible.

To calculate the probability of a repetition in the two letters, consider that there are 262 combinations, of which 26 X 25 do not contain repetitions. (There is free choice among 26 alternatives for the first letter, but only 25 choice for the following letter.) Therefore, the probability of a repetition within the two letters is (26)(25)/262 or 25/26.

The chance of a repeated digit within the four digit bloc is (10)(9)(8)(7)/104) or 504/1000.

If there is no repetition of a digit within either the two-digit bloc or the four-digit bloc, there is still a chance of repetition of a digit between the blocs. The chance of this is (8 X 7 X 6 x 5)/104 or 168/1000.

To reach the final answer, it is advantageous to calculate first the probability of not getting the specified repetition and then subtract this number from one. The probability of not getting a repetition in the first bloc is 9/10, and the probability of not getting a repetition between the first and second blocs is 168/1000. Therefore, the probability of not getting a repetition within the first bloc or between the first and the second number blocs is the product of these two, or 1512/10,000. Further multiplications by the independent probabilities of no repetition within the two remaining blocs yields a value of about 2.88 X 10-4. Therefore, the probability of at least one of the repetitions specified is about 0.999712.

Wiki User

13y ago