Question

a building security code has 2 numeric digits 0 through 9 followed by 2 letters. what is the probability that the first digit is nine an last letter is A?​

Answer 1

If we remove human choices in creating the code the answer is 10 (the possible choices) times 26 (the possible choices) so 260 is the probability

Answer 2

Answer: $\dfrac{1}{260}$

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 :-

$10\times10\times26\times26=67600$

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 :-

$1\times10\times26\times1=260$

Then, the probability that the first digit is nine an last letter is A :-

$=\dfrac{260}{67600}=\dfrac{1}{260}$

Hence, the probability that the first digit is nine an last letter is A= $\dfrac{1}{260}$