A computer system uses passwords that contain exactly eight characters, and each

Question

A computer system uses passwords that contain exactly eight characters, and each character is one of 26 lower-case letters (a-z) or 26 upper-case letters (A-Z) or 10 integers (0-9). Let Ohm denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Suppose that all passwords Ohm are equally likely. Determine the probability of each of the following: (a) A (b) B (c) A password contains at least 1 integer (d) A password contains exactly 2 integers.

Explanation / Answer

Total number of possible choices for each character is 62

( 26 upper-case letters + 26 lower case letters + 10 intergers )

Part a)

Password contain exactly 8 character.

A : Event that consist of passwords with only letters.

Total number of all possible passoword password =628

Total number of password with only letters =528

P(A)= 528 / 628

P(A) =0.2448

Part b)

B:   Event that consist of passwords with only integers

Total number of all possible passowords= 628

Total number of password with only integers are 108

P(B) =108 / 628

P(B) =0.000000458

Part c)

In part a ) we have already fount probability that password contain only letters (that is no interger)

P( password contain at least 1 integer ) = 1 - P( password contain only letters )

   = 1 - 0.2448=0.7552

P( password contain at least 1 integer ) = 0.7552

part D )

We have to find, P(password contain exactly 2 integer ) .

Total number of all possible passowords = 628

Number of possible password with 2 integer and 6 letters is 102 x 526

Total number of position for two integer = 8C2 = 28

P(password contain exactly 2 integer ) = 28x102 x 526/ 628

= 0.2535

P(password contain exactly 2 integer ) = 0.2535

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