Chapter 6.8, Problem 15E

To determine

To find : Your computer password has 4 capital letters followed by 4 digits. Your friend randomly chooses 4 capital letters and 4 digits. Use calculator to find the probability that your friend chooses your password.

Answer to Problem 15E

The probability that my friend chooses my password is $\frac{\text{1}}{4,569,760,000}$ .

Explanation of Solution

Given information :

Consider, the information provided in the question,

Computer password has 4 capital letters followed by 4 digits.

Calculation :

Use counting principle to find out the number of different combination. Therefore, the number of different combinations is

  $26\cdot 26\cdot 26\cdot 26\cdot 10\cdot 10\cdot 10\cdot 10=4,569,760,000$

Out of these combinations only 1 will be password. Therefore, probability that he chooses password is

  $\begin{array}{l}P\left(\text{Chooses Password}\right)=\frac{\text{Number of favaourable outcome}}{\text{Total number of outcome}}\\ P\left(\text{Chooses Password}\right)=\frac{\text{1}}{4,569,760,000}\end{array}$

Hence,

The probability that my friend chooses my password is $\frac{\text{1}}{4,569,760,000}$ .