Question

1. For a certain computer program a password must be exactly 5 characters long. The first character can be any lowercase letter, the second must be an uppercase letter, the third character must be a number from 0 – 9, the fourth character can either be a lowercase letter or a number 0 - 9, the fifth character has to be exactly the same as the first character.                                                                                         (6)
   1. How many possible passwords are there?

What is the probability of randomly guessing the password “dW9wd”?

Answer 1

Here,

In password there are tota 5 characters,

The first character can be lowercase letter,

There for there are 26 options for first character.

And the second character can be uppercase letter,

Therefore there are 26 possible options for second character.

The third character must be number from 0 -9

Therefore there are 10 possible option for third character.

And fourth character must be lowercase letter or number from 0-9

Therefore there are 36 possible option for fourth character.

And 5th character has exactly same as first

Hence there are only 1 possible option for 5th character.

Thus

Total possible passwords are

= 26*26*10*36*1

=243360

Thus total possible passwords are 243360.

Now

Probability of randomly guessing password "dW9wd" is,

=1/243360

=0.0000041