a building security code has 2 numeric digits, 0 through 9, followed by 2 letters. what is the probability…

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 and the last letter is a?

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 and the last letter is a?

Answer

Explanation:

Step1: Calculate digit - 1 probability

There are 10 possible digits (0 - 9). The probability that the first digit is 9 is $\frac{1}{10}$ since there is only 1 favorable outcome (the digit 9) out of 10 possible outcomes.

Step2: Calculate digit - 2 probability

There are 10 possible digits for the second - digit. The probability of any particular digit does not affect our desired event for now, and we consider it has 10 possible values.

Step3: Calculate first - letter probability

There are 26 letters in the alphabet. The probability of any letter is $\frac{1}{26}$.

Step4: Calculate second - letter probability

We want the second letter to be A. There are 26 letters in total, so the probability that the second letter is A is $\frac{1}{26}$.

Step5: Use the multiplication rule for independent events

Since the selection of digits and letters are independent events, the probability of the combined event is the product of the probabilities of each individual event. The probability $P=\frac{1}{10}\times1\times\frac{1}{26}\times\frac{1}{26}=\frac{1}{6760}$.

Answer:

$\frac{1}{6760}$