Question

a bank requires a four - digit access code for each account. the access code is generated using the digits 0 - 9, and the digits can be repeated. what is the probability of an access code \1234\?

1. $\frac{1}{10,000}$
2. $\frac{1}{6,561}$
3. $\frac{1}{10}$
4. $\frac{2}{5}$

Explanation:

Step1: Calculate total number of codes

Each digit has 10 choices (0 - 9), so for a 4 - digit code with repetition allowed, the total number of possible codes is $10\times10\times10\times10=10^4 = 10000$ by the multiplication principle.

Step2: Calculate probability

The probability of a specific code (in this case "1234") is the number of favorable outcomes (1) divided by the number of total outcomes. So the probability $P=\frac{1}{10000}$.

Answer:

$\frac{1}{10000}$