2
$\begingroup$

I'm having trouble with a question that seems to perplex: A number plate contains three letters followed by three numbers. A number plate is selected at random. Calculate the probability that the number plate selected begins with the letters AAA. I already know the total amount of possible combinations there are, do I just subtract the possibility of not getting three A's from 1?

$\endgroup$
  • 2
    $\begingroup$ Since you are new, I want to give some advice about the site: To get the best possible answers, you should explain what your thoughts on the problem are so far. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people tend to be more willing to help you if you show that you've tried the problem yourself. Some would consider your post rude because it just demands an answer, instead of requesting help, so please consider rewriting. $\endgroup$ – Zev Chonoles May 18 '13 at 7:34
  • 3
    $\begingroup$ There is a problem of interpretation. Does a plate consist of $3$ letters and $3$ digits in any order, like 7C99XK, or is it $3$ letters followed* by $3$ digits? The answers will be different. $\endgroup$ – André Nicolas May 18 '13 at 7:57
  • 1
    $\begingroup$ Eventual answers will probably be based on the 26 letters of the English alphabet. If you are working under a different assumption, you may want to comment on that or (may be preferrably!) modify the given answers to your setting. $\endgroup$ – Jyrki Lahtonen May 18 '13 at 8:06
  • 1
    $\begingroup$ Hint: can you calculate the number of plates that do begin with AAA? I would think that is an easier question than the total number of plates! $\endgroup$ – Jyrki Lahtonen May 18 '13 at 8:08
  • 1
    $\begingroup$ Great! You may consider posting your own solutions as an answer (I guess that there is a time limit or may be not - I don't know the rule). That way you get feedback on your answer, and, if correct, also upvotes :-). Welcome to the forum. Hope you stay. $\endgroup$ – Jyrki Lahtonen May 18 '13 at 8:47
0
$\begingroup$
I already know the total amount of possible combinations there are, 
do I just subtract the possibility of not getting three A's from 1?

There are 26 x 26 x26 possible combinations of three characters from A-Z = 17,576

 Calculate the probability that the number plate selected 
 begins with the letters AAA

The probability is 1 in 17,576, or 5,689576695493855e-5

Btw, this implies that all letter combinations are issued equally. Some countries, for instance, do not issue the letter Q as it is easily confused with O. Also, some countries use the first one or two letters to indicate the city of issue, so some combinations may never occur (perhaps those containing an X or Z, etc, depending on country).

In fact, you can't really calculate the probability at all unless the question explicitly states that you are drawing a random plate form a pile which contains exactly one plate each of the complete sequence from AAA 1 to ZZZ 999.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.