Question

Employee identification codes at a company contain 2 letters followed by 4 digits. Assume that all codes areequally likely. Identify the probability that an ID code does not contain the letter o

Answer 1

$\begin{gathered} \text{For total }ID\text{ codes} \\ \text{There are 26 letters, and 10 digits} \\ ID\text{ code = l}etter,\text{ letter, digit, digit, digit, digit} \\ \text{Total codes = 26}\cdot26\cdot10\cdot10\cdot10\cdot10 \\ \text{Total codes = 6760000} \\ For\text{ }ID\text{ codes }without\text{ l} \\ 26-1=25 \\ ID\text{ codes }without\text{ l= 25}\cdot25\cdot10\cdot10\cdot10\cdot10 \\ ID\text{ codes }without\text{ l= 6250000} \\ P(ID\text{ codes }without\text{ l})=\frac{ID\text{ codes }without\text{ l}}{\text{Total codes}} \\ \\ P(ID\text{ codes }without\text{ l})=\frac{\text{6250000}}{\text{6760000}}=0.9246 \\ \\ \text{The probability of }an\text{ ID code doesn´t contain }a\text{ letter l is }0.9246 \end{gathered}$