Answer: [tex]\dfrac{1}{260}[/tex]
Step-by-step explanation:
Given : A building security code has 2 numeric digits 0 through 9 followed by 2 letters.
Total digits (0,1,2,3,4,5,6,7,8,9)= 10
Total letters in English Alphabet = 26
Then, the total number of ways to make a code if repetition is allowed :-
[tex]10\times10\times26\times26=67600[/tex]
The number of ways to make a code with first digit is nine an last letter is A (we fix first position for 9 as 1 and the last position for a as 1) , if repetition is allowed :-
[tex]1\times10\times26\times1=260[/tex]
Then, the probability that the first digit is nine an last letter is A :-
[tex]=\dfrac{260}{67600}=\dfrac{1}{260}[/tex]
Hence, the probability that the first digit is nine an last letter is A= [tex]\dfrac{1}{260}[/tex]
