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Bonnie created a website where users could randomly generate a ＂strong password.＂ She claims that 69%69\% of generated passwords contain at least one capital letter, number, and symbol.\newlineIf the claim is correct, and a user randomly generates 22 passwords on the website, what is the probability that 00 of the passwords contain at least one capital letter, number, and symbol?\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____\newline

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Q. Bonnie created a website where users could randomly generate a ＂strong password.＂ She claims that 69%69\% of generated passwords contain at least one capital letter, number, and symbol.\newlineIf the claim is correct, and a user randomly generates 22 passwords on the website, what is the probability that 00 of the passwords contain at least one capital letter, number, and symbol?\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____\newline
  1. Find Probability: First, we need to find the probability that a password does not contain at least one capital letter, number, and symbol. Since 69%69\% of passwords do contain these, the probability that a password does not contain them is 100%−69%=31%100\% - 69\% = 31\%.
  2. Convert to Decimal: Now, we convert this percentage to a decimal to make calculations easier. So, 31%31\% as a decimal is 0.310.31.
  3. Calculate Probability: Next, we calculate the probability that both passwords generated do not contain at least one capital letter, number, and symbol. Since the events are independent, we multiply the probability of one password not having these features by itself. So, 0.31×0.310.31 \times 0.31.
  4. Multiply Probabilities: Doing the multiplication, we get 0.31×0.31=0.09610.31 \times 0.31 = 0.0961.
  5. Round Result: Finally, we round the result to the nearest thousandth as instructed. The rounded decimal is 0.0960.096.

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