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A spyware is trying to break into a system by guessing its password. It does not give up until it tries 1 million different passwords. What is the probability that it will guess the password and break in if by rules, the password must consist of

Sagot :

MrRoyal

Answer:

[tex]Probability = 0.006033[/tex]

Step-by-step explanation:

Given

[tex]Tries = 1000000[/tex]

Required

Determine the probability of 6 different lower case letters (Question continuation)

There are 26 lower case letters.

The first can be any of letters 26

The second can be any of letters 26 - 1

The third can be any of letters 26 - 2

The fourth can be any of letters 26 - 3

The fifth can be any of letters 26 - 4

The sixth can be any of letters 26 - 5

Number of selection is:

[tex]Selection = 26 * (26 - 1) * (26 - 2) * (26 - 3) * (26 - 4) * (26 - 5)[/tex]

[tex]Selection = 26 * 25 * 24 * 23 * 22 * 21[/tex]

[tex]Selection = 165765600[/tex]

The probability is:

[tex]Probability = \frac{Tries}{Selection}[/tex]

[tex]Probability = \frac{1000000}{165765600}[/tex]

[tex]Probability = 0.00603261472[/tex]

[tex]Probability = 0.006033[/tex] --- approximated

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