Question

A computer is generating passwords. The computer generates ten characters at random, and each is equally likely to be any of the letters or digits. Replications are allowed. What is the probability that the password will contain all letters? Round your answers to four decimal places.

Answer 1

Answer: 0.0386

Step-by-step explanation:

Number of digits = 10

Number of letters in English alphabet = 26

Total number of characters = $10+26=36$

Now, if replication is allowed, then the total number of ways to make a ten character password will be :_

$(36)^{10}$

The number of ways to make a password having all letters :-

$(26)^{10}$

Now, the probability that the password will contain all letters will be :-

$\dfrac{26^{10}}{36^{10}}=0.0386107708316\approx0.0386$

Hence, the probability that the password will contain all letters =0.0386