Question: All-Numeric Passwords. The technology consultancy DataGenetics published the online document PIN analysis. In addition to analyzing PIN numbers, password trends were examined. Seven million all-numeric

All-Numeric Passwords. The technology consultancy DataGenetics published the online document PIN analysis. In addition to analyzing PIN numbers, password trends were examined. Seven million all-numeric passwords were collected and yielded the following estimate of the probability distribution of the number of digits used in an all-numeric password.

Digits Probability Digits Probability 4 0.492 9 0.029 5 0.092 10 0.015 6 0.178 11 0.004 7 0.073 12 0.003 8 0.113 13 0.001

a. Explain why the probabilities in the table provide only an estimate of the true probabilities.

b. Estimate the probability that an all-numeric password contains at least six digits.

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