SOLUTION: 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 letters followed by two numerals followed by three letter

Algebra ->  Probability-and-statistics -> SOLUTION: 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 letters followed by two numerals followed by three letter      Log On


   

Question 482230: 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 letters followed by two numerals followed by three letters? (Round to the nearest whole percent.)
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
We find the probability of the complement event and subtract from 1.

So we first calculate the probability of having no repetitions:

The number of tags with no repetitions is

26×25×10×9×8

The number of possible tags:

26×26×10×10×10

So the probability is

%2826%2A25%2A10%2A9%2A8%29%2F%2826%2A26%2A10%2A10%2A10%29 =

 =

%2825%2A9%2A8%29%2F%2826%2A10%2A10%29 =

%28%285%2A5%29%2A%283%2A3%29%2A%282%2A2%2A2%29%29%2F%28%2813%2A2%29%285%2A2%29%285%2A2%29%29 =

 =

%283%2A3%29%2F13

9%2F13

Now to find the desired probability, we subtract that from 1.

1-9%2F13=13%2F13-9%2F13=4%2F13

That's the exact fraction answer.  But you wanted the decimal
value 

.3076923077+=%2230.76923077%25%22

and you want it rounded to the nearest whole percent. 

So it's 31%.

Edwin