Questions: Find the probability that none of the selected adults say that they were too young to get tattoos (Round to four decimal places as needed)

Find the probability that none of the selected adults say that they were too young to get tattoos (Round to four decimal places as needed)
Transcript text: a. Find the probability that none of the selected adults say that they were too young to get tattoos $\square$ (Round to four decimal places as needed)
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Solution

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Solution Steps

Step 1: Define the Problem

We need to find the probability that none of the selected adults say that they were too young to get tattoos. This can be modeled using a binomial distribution where:

  • \( n = 25 \) (the number of trials, or selected adults),
  • \( x = 0 \) (the number of successes, or adults saying they were too young),
  • \( p = 0.29 \) (the probability of success, or saying they were too young),
  • \( q = 1 - p = 0.71 \) (the probability of failure, or not saying they were too young).
Step 2: Apply the Binomial Probability Formula

The probability of exactly \( x \) successes in \( n \) trials is given by the formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

Substituting the values into the formula:

\[ P(X = 0) = \binom{25}{0} \cdot (0.29)^0 \cdot (0.71)^{25} \]

Step 3: Calculate the Probability

Calculating each component:

  • \( \binom{25}{0} = 1 \)
  • \( (0.29)^0 = 1 \)
  • \( (0.71)^{25} \approx 0.0002 \)

Thus, we have:

\[ P(X = 0) = 1 \cdot 1 \cdot 0.0002 = 0.0002 \]

Final Answer

The probability that none of the selected adults say they were too young to get tattoos is:

\[ \boxed{0.0002} \]

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