Question

In: Statistics and Probability

question : (buildings password) The building has an electronic lock ..the password fo it is in...

question :

(buildings password)

The building has an electronic lock ..the password fo it is in shape NNNNN, where N is one of the numbers 0,1,.....9. calculate the numbers of possible password when password creation is restricted by the following terms:

(a) no number must be repeated in the password

(b) there must be apair in the password , exactly two of the same number with all other numbers being different ..for examole(23783)

assuming that passwords are generated randomly from all possible passwords, calculate the probabilities of the following events:

(a)no number is repeated inthe password

(b) the password is a couple (as above)

Expert Solution

a) The number of passwords possible here would be computed as:

_ _ _ _ _

As there are 10 digits in total, therefore the total number of passwords possible here would be given as the number of permutation of 10 digits taken 5 at a time. Therefore the number of passwords possible here are computed as:

= 10*9*8*7*6

= 30240

b) The number of passwords possible here such that exactly two of the same number with all other numbers being different is computed as:

= Number of ways to select 4 of the 10 digits * Number of ways to select one of those 4 digits that would be repeated * Number of permutations

______________________________________________________________________________________

Total number of possible passwords without any condition = 10⁵ = 100000

a) Probability that a password is selected such that no number is repeated

= 30240 / 100000

= 0.3024

Therefore 0.3024 is the required probability here.

b) Probability that the password is a couple

= 50400 / 100000

= 0.5040

Therefore 0.5040 is the required probability here.

orchestra answered 2 years ago

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