Final answer:
The correct answer is option C. 1/260.The probability of a building security code having a first digit of nine and the last letter A is 1/260, calculated by the individual probabilities of getting a nine (1/10) and letter A (1/26).
Step-by-step explanation:
To find the probability that the first digit is nine and the last letter is A for a building security code that has 2 numeric digits followed by 2 letters, we multiply the individual probabilities of each event. There are 10 possible digits (0-9) for each numeric position and 26 possible letters (A-Z) for each alphabetic position.
The probability that the first digit is nine is 1/10 because there is only one nine out of ten possible digits. The probability that the second digit is any number is 1 because it can be any digit from 0 to 9. The probability that the first letter is any letter is also 1 because it can be any letter from A to Z. Finally, the probability that the last letter is A is 1/26, since there is only one A out of twenty-six possible letters. Multiplying these probabilities together gives:
(1/10) * 1 * 1 * (1/26) = 1/260.